Persons: Karachik, Valeriy Valentinovich

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Karachik, Valeriy Valentinovich

Total publications:	144 (126)
in MathSciNet:	72 (72)
in zbMATH:	68 (58)
in Web of Science:	61 (61)
in Scopus:	75 (75)
Cited articles:	73
Citations:	809
Presentations:	1

Number of views:
This page:	8665
Abstract pages:	21337
Full texts:	7555
References:	3436

Senior Researcher

Doctor of physico-mathematical sciences (2001)

Speciality:

01.01.02 (Differential equations, dynamical systems, and optimal control)

E-mail:

Keywords:

partial differential equations, boundary value problems, polynomial solutions, polyharmonic functions, Greens function, special polynomials and functions.

UDC:

517.956.22, 517.956, 517.956.225, 517.572, 517.575

MSC:

35C05, 35C10, 35C11, 35J05, 35J40, 31B30, 11B37

Subject:

Representations of solutions to boundary value problems for partial differential equations: solutions in closed form, series solutions, integral representations of solutions, Green's function.

Biography

1977 — graduated with honor from Tashkent State University.
1977–1978 — engineer, Institute of Cybernetics of Academy of Sciences of Uzbekistan;
1988 — Candidates degree, Institute of Mathematics of Academy of Sciences of Uzbekistan;
1991 — academic rank Senior Researcher;
1996 — Head of a Department, Institute of Cybernetics;
1996–1999 — Senior Researcher, University of World Economy and Diplomacy (UWED), Tashkent;
2000–2003 — Director of Computerized Testing Center, UWED;
2001 — Doctorates degree, Institute of Mathematics of Academy of Sciences of Uzbekistan;
2004–2011 — Professor, Department of Mathematical Analysis, South Ural State University, Chelyabinsk, Russia;
2011–2012 — Head of the Department of Differential Equations and Dynamical Systems, SUSU;
2013 — Head of the Department of Mathematical Analysis, SUSU;
09.2013 — Professor, Department of Mathematical and Functional Analysis, SUSU;
2016 — Professor, Department of Mathematical Analysis and Methods of Teaching Mathematics, SUSU;

Member of American Mathematical Society (1997) and European Mathematical Society; Reviewer of Mathematical Reviews (1997), Zentralblatt fur Mathematik (1992).

Main publications:

V. V. Karachik, “A problem for the polyharmonic equation in the sphere”, Siberian Mathematical Journal, 32:5 (1991), 767–774
V. V. Karachik, “Polynomial solutions to the systems of partial differential equations with constant coefficients”, Yokohama Math. J., 47 (2000), 121–142
V. V. Karachik, Method of normalized systems of functions, Publishing Center of SUSU, Chelyabinsk, 2014
V. V. Karachik, “Construction of Polynomial Solutions to the Dirichlet Problem for the Polyharmonic Equation in a Ball”, Computational Mathematics and Mathematical Physics, 54:7 (2014), 1122–1143
V. V. Karachik, “On Green function of the Dirichlet problem for polyharmonic equation in the ball”, Axioms, 12:6 (2023), 543

https://www.mathnet.ru/eng/person28783

https://scholar.google.com/citations?user=HPhjUpoAAAAJ&hl=en

https://zbmath.org/authors/ai:karachik.valery-v

https://mathscinet.ams.org/mathscinet/MRAuthorID/248313

https://elibrary.ru/author_items.asp?spin=7397-3067

ISTINA

https://istina.msu.ru/workers/134244389

https://orcid.org/0000-0002-3077-3595

https://www.webofscience.com/wos/author/record/J-6880-2016

https://www.scopus.com/authid/detail.url?authorId=6602898763

https://www.researchgate.net/profile/Valery_Karachik

Full list of publications:

scientific publications

by years

by types

by times cited

common list

		Citations (Crossref Cited-By Service + Math-Net.Ru)

1.	V. V. Karachik, “Construction of polynomial solutions to some boundary value problems for Poisson's equation”, Computational Mathematics and Mathematical Physics, 51:9 (2011), 1567-1587
2.	V. V. Karachik, “Normalized system of functions with respect to the Laplace operator and its applications”, J. Math. Anal. Appl., 287:2 (2003), 577–592	38 ^[x]
3.	V. V. Karachik, “Construction of Polynomial Solutions to the Dirichlet Problem for the Polyharmonic Equation in a Ball”, Computational Mathematics and Mathematical Physics, 54:7 (2014), 1122–1143
4.	V. V. Karachik, “On solvability conditions for the Neumann problem for a polyharmonic equation in the unit ball”, Journal of Applied and Industrial Mathematics, 8:1 (2014), 63–75
5.	V. V. Karachik, “A problem for the polyharmonic equation in the sphere”, Siberian Mathematical Journal, 32:5 (1991), 767–774
6.	V. V. Karachik, “Riquier-Neumann Problem for the Polyharmonic Equation in a Ball”, Differential Equations, 54:5 (2018), 648–657
7.	V. V. Karachik, “A Neumann-type problem for the biharmonic equation”, Siberian Advances in Mathematics, 27:2 (2017), 103–118	28 ^[x]
8.	V. V. Karachik, “A Neumann-type problem for the biharmonic equation”, Siberian Adv. Math., 27:2 (2017), 103–118
9.	V. V. Karachik, “On an Expansion of Almansi Type”, Math. Notes, 83:3 (2008), 335–344
10.	V. V. Karachik, “On one set of orthogonal harmonic polynomials”, Proceedings of American Mathematical Society, 126:12 (1998), 3513-3519	26 ^[x]
11.	V. V. Karachik, A. M. Sarsenbi, B. Kh. Turmetov, “On the solvability of the main boundary value problems for a nonlocal Poisson equation”, Turkish Journal of Mathematics, 43 (2019), 1604–1625	23 ^[x]
12.	V. V. Karachik, B. K. Turmetov, B. T. Torebek, “On some integro-differential operators in the class of harmonic functions and their applications”, Siberian Adv. Math., 22:2 (2012), 115–134
13.	V. V. Karachik, “Solution of the Dirichlet Problem with Polynomial Data for the Polyharmonic Equation in a Ball”, Differential Equations, 51:8 (2015), 1033–1042
14.	V. V. Karachik, “On the Arithmetic Triangle Arising from the Solvability Conditions for the Neumann Problem”, Math. Notes, 96:2 (2014), 217–227
15.	V. V. Karachik, B. T. Torebek, “On the Dirichlet–Riquier Problem for Biharmonic Equations”, Mathematical Notes, 102:1 (2017), 31–42
16.	V. V. Karachik, “Solvability Conditions for the Neumann Problem for the Homogeneous Polyharmonic Equation”, Differential Equations, 50:11 (2014), 1449–1456
17.	V. V. Karachik, “On One Representation of Analytic Functions by Harmonic Functions”, Siberian Adv. Math., 18:2 (2008), 103–117
18.	V. V. Karachik, “On the mean value property for polyharmonic functions in the ball”, Siberian Advances in Mathematics, 24:3 (2014), 169–182
19.	V. V. Karachik, N. A. Antropova, “On the solution of a nonhomogeneous polyharmonic equation and the nonhomogeneous Helmholtz equation”, Differential Equations, 46:3 (2010), 387–-399
20.	V. V. Karachik, “On some special polynomials”, Proceedings of American Mathematical Society, 132:4 (2004), 1049-1058	19 ^[x]
21.	V. V. Karachik, N. A. Antropova, “Polynomial solutions of the Dirichlet problem for the biharmonic equation in the ball”, Differential Equations, 49:2 (2013), 251–256
22.	V. Karachik, “Greens function of Dirichlet problem for biharmonic equation in the ball”, Complex Variables and Elliptic Equations, 64:9 (2019), 1500–1521 https://www.tandfonline.com/eprint/U28xHRrDURAMce7APwn9/full?target=10.1080/17476933.2018.1536702	14 ^[x]
23.	V. V. Karachik, “The Green Function of the Dirichlet Problem for the Triharmonic Equation in the Ball”, Mathematical Notes, 107:1 (2020), 105–120
24.	V. Karachik, B. Turmetov, “On solvability of some nonlocal boundary value problems for biharmonic equation”, Mathematica Slovaca, 70:2 (2020), 329–342	13 ^[x]
25.	V. V. Karachik, B. Kh. Turmetov, “On Green’s function of the Robin problem for the Poisson equation”, Advances in Pure and Applied Mathematics, 10:3 (2019), 203–214	13 ^[x]
26.	V. V. Karachik, “The Green Function of the Dirichlet Problem for the Biharmonic Equation in a Ball”, Computational Mathematics and Mathematical Physics, 59:1 (2019), 66–81
27.	V. V. Karachik, B. Kh. Turmetov, “On the Green’s Function for the Third Boundary Value Problem”, Siberian Advances in Mathematics, 29:1 (2019), 32–43
28.	V. V. Karachik, “Green’s Functions of the Navier and Riquier–Neumann Problems for the Biharmonic Equation in the Ball”, Differential Equations, 57:5 (2021), 654–668 https://link.springer.com/article/10.1134/S0012266121050098
29.	Karachik V.V., Antropova N.A., “O polinomialnykh resheniyakh zadachi Dirikhle dlya bigarmonicheskogo uravneniya v share”, Sibirskii zhurnal industrialnoi matematiki, XV:2, (50) (2012), 86-98	12 ^[x]
30.	V. V. Karachik, “Dirichlet and Neumann boundary value problems for the polyharmonic equation in the unit ball”, Mathematics, 9:16 (2021), 1907	11 ^[x]
31.	V. V. Karachik, B. Kh. Turmetov, “On solvability of some boundary value problems for a biharmonic equation with periodic conditions”, Filomat, 32:3 (2018), 947–953	10 ^[x]
32.	V. V. Karachik, “Generalized Third Boundary Value Problem for the Biharmonic Equation”, Differential Equations, 53:6 (2017), 756–765
33.	V. V. Karachik, “Method for constructing solutions of linear ordinary differential equations with constant coefficients”, Comput. Math. Math. Phys., 52:2 (2012), 219–234
34.	B. Turmetov, V. Karachik, “On Eigenfunctions and Eigenvalues of a Nonlocal Laplace Operator with Multiple Involution”, Symmetry, 13:10 (2021), 1781	9 ^[x]
35.	Valery V. Karachik, “Polynomial solutions to Dirihlet boundary value problem for the $3$-harmonic equation in a ball”, J. Sib. Fed. Univ. Math. Phys., 5:4 (2012), 527–546
36.	V. Karachik, B. Turmetov, H. Yuan, “Four Boundary Value Problems for a Nonlocal Biharmonic Equation in the Unit Ball”, Mathematics, 10:7 (2022), 1-21 https://www.mdpi.com/2227-7390/10/7/1158#	8 ^[x]
37.	V. V. Karachik, B. Kh. Turmetov, A. Bekaeva, “Solvability of some boundary-value problems for polyharmonic equation with Hadamard-Marchaud boundary operator”, Russian Mathematics, 58:7 (2014), 11–24
38.	V. V. Karachik, “Polinomialnye resheniya differentsialnykh uravnenii v chastnykh proizvodnykh s postoyannymi koeffitsientami I”, Vestn. Yuzhno-Ur. un-ta. Ser. Matem. Mekh. Fiz., 2011, no. 4, 4–17	8 ^[x]
39.	V. V. Karachik, “Class of Neumann-Type Problems for the Polyharmonic Equation in a Ball”, Computational Mathematics and Mathematical Physics, 60:1 (2020), 144–162
40.	B. Turmetov, V. Karachik, M. Muratbekova, “On a boundary value problem for the biharmonic equation with multiple involution”, Mathematics, 9:17 (2021), 2020 https://doi.org/10.3390/math9172020	6 ^[x]
41.	V. V. Karachik, “Green Function of the Dirichlet Boundary Value Problem for Polyharmonic Equation in a Ball Under Polynomial Data”, Izv. Saratov. Univ. Mat. Mekh. Inform., 14:4(2) (2014), 550–558
42.	V. V. Karachik, “On some special polynomials and functions”, Sib. Èlektron. Mat. Izv., 10 (2013), 205–226
43.	B. Kh. Turmetov & V. V. Karachik, “Solvability of nonlocal Dirichlet problem for generalized Helmholtz equation in a unit ball”, Complex Variables and Elliptic Equations, 68:7 (2023), 1204–1218 https://www.tandfonline.com/eprint/BURHNJX3TJI4JHBQ4TIG/full?target=10.1080/17476933.2022.2040021	4 ^[x]
44.	V. V. Karachik, “Solving a Problem of Robin Type for Biharmonic Equation”, Russian Mathematics, 62:2 (2018), 34–48 https://rdcu.be/bqQ8z
45.	V. V. Karachik, “Riquier–Neumann Problem for the Polyharmonic Equation in a Ball”, Mathematics, 11:4 (2023), 1000 https://www.mdpi.com/2227-7390/11/4/1000	3 ^[x]
46.	V. V. Karachik, “Integral identities on a sphere for normal derivatives of polyharmonic functions”, SIBERIAN ELECTRONIC MATHEMATICAL REPORTS, 14 (2017), 533–551
47.	V. V. Karachik, B. T. Torebek, “On one mathematical model described by boundary value problem for the biharmonic equation”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 9:4 (2016), 40–52	3 ^[x]
48.	V. V. Karachik, “Polynomial solutions to partial differential equations with constant coefficients II”, Vestn. Yuzhno-Ural. Gos. Un-ta. Ser. Matem. Mekh. Fiz., 2011, no. 5, 27–38
49.	V. V. Karachik, “Almansi decompositions for non-singular second order partial differential operators”, Vestn. Yuzhno-Ural. Gos. Un-ta. Ser. Matem. Mekh. Fiz., 2010, no. 3, 4–12
50.	V. V. Karachik, “A problem with higher-order normal derivatives on the boundary for the Poisson equation”, Differential Equations, 32:3 (1996), 421–424
51.	B. Kh. Turmetov, V. V. Karachik, “On solvability of some inverse problems for a nonlocal fourth-order parabolic equation with multiple involution”, AIMS Mathematics, 9:3 (2024), 6832–6849	2 ^[x]
52.	V. V. Karachik, “The Green function of the Navier problem for the polyharmonic equation in a ball”, Journal of Mathematical Sciences, 269:2 (2023), 189–204 https://rdcu.be/c5Sii	2 ^[x]
53.	V. V. Karachik, “Sufficient Conditions for Solvability of One Class of Neumann-Type Problems for the Polyharmonic Equation”, Computational Mathematics and Mathematical Physics, 61:8 (2021), 1276–1288 http://link.springer.com/article/10.1134/S0965542521040059
54.	V. Karachik, B. Turmetov, “Solvability of one nonlocal Dirichlet problem for the Poisson equation”, Novi Sad Journal of Mathematics, 50:1 (2020), 67–88 https://www.dmi.uns.ac.rs/nsjom/paper.html?noid=ns8942	2 ^[x]
55.	V. V. Karachik, B. T. Torebek, “On an Uniqueness and Correct Solvability of the Biharmonic Boundary Value Problem”, ICAAM 2016 (Almaty, Kazakhstan September 7-10, 2016), AIP Conference Proceedings, 1759, 2016, 020045-1 020045-4	2 ^[x]
56.	V. V. Karachik, “Application of the Almansi formula for constructing polynomial solutions to the Dirichlet problem for a second-order equation”, Russian Math. (Iz. VUZ), 56:6 (2012), 20–29
57.	V. V. Karachik, S. Abdoulaev, “Construction of polynomial solutions to the Dirichlet boundary value problem for the 3-harmonic equation in the unit ball”, Pure and Applied Mathematics Journal, 1:1 (2012), 1-9 https://www.sciencepublishinggroup.com/journal/archive?journalid=141&issueid=1410101	2 ^[x]
58.	V. V. Karachik, “O pazpeshimosti kpaevoi zadachi dlya upavneniya Gelmgoltsa s nopmalnymi ppoizvodnymi vysokogo popyadka na gpanitse”, Differentsialnye uravneniya, 28:5 (1992), 907–909	2 ^[x]
59.	V. V. Karachik, “Postpoenie polinomialnykh peshenii diffepentsialnykh upavnenii s postoyannymi koeffitsientami”, Differentsialnye uravneniya, 27:3 (1991), 534–535	2 ^[x]
60.	V. V. Karachik, “On Green function of the Dirichlet problem for polyharmonic equation in the ball”, Axioms, 12:6 (2023), 543 https://www.mdpi.com/2075-1680/12/6/543	1 ^[x]
61.	V. V. Karachik, “Green's functions of some boundary value problems for the biharmonic equation”, Complex Variables and Elliptic Equations, 67:7 (2022), 1712–1736	1 ^[x]
62.	B. Kh. Turmetov, V. V. Karachik, “Neumann boundary condition for a nonlocal biharmonic equation”, Bulletin of the South Ural State University, Ser. Mathematics. Mechanics. Physics, 14:2 (2022), 51–58 https://vestnik.susu.ru/mmph/article/view/11942
63.	B. Turmetov, V. Karachik, “Construction of Eigenfunctions to One Nonlocal Second-Order Differential Operator with Double Involution”, Axioms, 11:10 (2022), 543 https://www.mdpi.com/2075-1680/11/10/543	1 ^[x]
64.	B. Kh. Turmetov, V. V. Karachik, “O zadache Dirikhle dlya nelokalnogo poligarmonicheskogo uravneniya”, Vestnik Yuzhno-Uralskogo gosudarstvennogo universiteta. Seriya: Matematika. Mekhanika. Fizika., 13:2 (2021), 37–45	1 ^[x]
65.	B.Kh. Turmetov, V.V. Karachik, “O razreshimosti kraevykh zadach Dirikhle i Neimana dlya uravneniya Puassona s mnozhestvennoi involyutsiei”, Vestnik Udmurtskogo universiteta. Matematika. Mekhanika. Kompyuternye nauki, 31:4 (2021), 651–667	1 ^[x]
66.	V. V. Karachik, “Predstavlenie resheniya zadachi Dirikhle dlya bigarmonicheskogo uravneniya v share cherez funktsiyu Grina”, Chelyabinskii fiziko-matematicheskii zhurnal, 5:4-1 (2020), 391–399	1 ^[x]
67.	H. Yuan, V. V. Karachik, “Representations of super-holomorphic functions and their applications”, Complex Variables and Elliptic Equations, 61:11 (2016), 1517–1532	1 ^[x]
68.	V. V. Karachik, S. K. Masanov, B. Kh. Turmetov, “On solvability of some boundary value problems for a biharmonic equation with periodic conditions”, AIP Conference Proceedings, 1759:020118 (2016), 020118-1-020118-6 http://dx.doi.org/10.1063/1.4959732	1 ^[x]
69.	V. V. Karachik, “Cauchy and Goursat problems for differential equation of third order”, Vestn. Yuzhno-Ural. Gos. Un-ta. Ser. Matem. Mekh. Fiz., 7:2 (2015), 31–43
70.	V. V. Karachik, Hong Fen, Yuan, “Dunkl-Poisson Equation and Related Equations in Superspace”, Mathematical Modelling and Analysis, 20:6 (2015), 768–-781 http://www.tandfonline.com/doi/abs/10.3846/13926292.2015.1112856	1 ^[x]
71.	V. V. Karachik, “On an arithmetical triangle”, Journal of Mathematical Sciences, 195:5 (2013), 665–675	1 ^[x]
72.	V. V. Karachik, “Polynomial Solutions to the Lamé Equations”, Siberian Adv. Math., 13:2 (2003), 66–79
73.	V. V. Karachik, “Harmonic polynomials and the divisibility problem”, PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 125:11 (1997), 3257–3258	1 ^[x]
74.	Hongfen Yuan; Valery Karachik, “Solutions of Umbral Dirac-Type Equations”, Mathematics, 12:2 (2024), 344 https://doi.org/10.3390/math12020344
75.	V. V. Karachik, “Green’s Function of the Riquier–Neumann Problem for the Polyharmonic Equation in the Unit Ball”, Computational Mathematics and Mathematical Physics, 64:5 (2024), 1015–1028 https://rdcu.be/dKLLV
76.	M. Muratbekova, V. Karachik, B. Turmetov, “Bitsadze-Samarsky type problems with double involution”, Boundary Value Problems, 2024:86 (2024), 1-21
77.	V. V. Karachik, “Bigarmonicheskaya zadacha Neimana s dvoinoi involyutsiei”, Vestnik YuUrGU. Seriya «Matematika. Mekhanika. Fizika», 16:3 (2024), 18–26
78.	V. V. Karachik, “Razreshimost zadachi Neimana dlya poligarmonicheskogo uravneniya v share”, Trudy MFTI, 16:2 (2024), 64–76 https://www.elibrary.ru/download/elibrary_68579514_24454934.pdf
79.	V. Karachik, “Solvability of the Neumann Boundary Value Problem for the Polyharmonic Equation in a Ball”, Lobachevskii Journal of Mathematics, 45:8 (2024), 3559–3571 (to appear)
80.	V. V. Karachik, “Funktsiya Grina zadachi Rike-Neimana dlya poligarmonicheskogo uravneniya v edinichnom share”, Zhurnal vychislitelnoi matematiki i matematicheskoi fiziki, 64:5 (2024), 791–803
81.	V. V. Karachik, “Reshenie zadachi Rike–Neimana dlya poligarmonicheskogo uravneniya v share”, Vestnik YuUrGU. Seriya «Matematika. Mekhanika. Fizika», 15:1 (2023), 26–33
82.	H. Yuan, V. Karachik, “Dirichlet and Neumann Boundary Value Problems for Dunkl Polyharmonic Equations”, Mathematics, 11:9 (2023), 2185 https://www.mdpi.com/2227-7390/11/9/2185
83.	V. V. Karachik, “Representation of the Green’s Function of the Dirichlet Problem for the Polyharmonic Equation in the Ball”, Differential Equations, 59:8 (2023), 1061–1074 https://rdcu.be/dnV75
84.	V. V. Karachik, “On one integral representation of solutions of polyharmonic equation”, Lobachevskii Journal of Mathematics, 44:7 (2023), 2749–2756 https://rdcu.be/dpI0k
85.	B. Turmetov, V. Karachik, “On eigenfunctions and eigenvalues of a nonlocal Laplace operator with involution in a parallelepiped”, Sixth international conference of mathematical sciences (ICMS 2022) (Istanbul, Turkey, 20–24 July 2022), AIP Conference Proceedings, 2879, no. 1, 2023, 040005-1–040005-4
86.	H. Yuan, V. Karachik, “Solutions of the generalized Dirichlet problem for the iterated slice Dirac equation”, Czechoslovak Mathematical Journal, 72:147 (2022), 523–539
87.	V. V. Karachik, “Solution to the Dirichlet Problem for the Polyharmonic Equation in the Ball”, Siberian Advances in Mathematics, 32:3 (2022), 197–210 https://rdcu.be/cUSbv
88.	V. V. Karachik, “Reshenie zadachi Neimana dlya poligarmonicheskogo uravneniya v edinichnom share”, Sistemy kompyuternoi matematiki i ikh prilozheniya, 2022, no. 23, 241–246
89.	V. Karachik, B. Turmetov, “On Solvability of Some Boundary Value Problems with Involution for the Biharmonic Equation”, Springer Proceedings in Mathematics and Statistics, 4th International Conference on Analysis and Applied Mathematics, ICAAM 2018 (Mersin, 6 September 2018 - 9 September 2018, 262329), 351, Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 351), 2021, 75–90 https://link.springer.com/chapter/10.1007/978-3-030-69292-6_5
90.	B. Turmetov, V. Karachik, “On Sufficient Solvability Conditions For Neumann Type Problems For Polyharmonic Equation In A Ball”, AIP Conference Proceedings (Uzbekistan-Malaysia international online conference on “Computational models and technologies” (CMT 2020)), 2365, AIP Publishing, 2021, 060002 https://aip.scitation.org/doi/abs/10.1063/5.0057206
91.	V. V. Karachik, “Reshenie zadachi Dirikhle dlya poligarmonicheskogo uravneniya v share”, Matem. tr., 24:2 (2021), 46–64
92.	V. V. Karachik, “Usloviya razreshimosti zadachi Neimana $N_2$ dlya poligarmonicheskogo uravneniya v share”, Vestnik Yuzhno-Uralskogo gosudarstvennogo universiteta. Seriya: Matematika. Mekhanika. Fizika., 12:2 (2020), 13–20
93.	V. V. Karachik, “Neumann type problems for the polyharmonic equation in ball”, Journal of Mathematical Sciences, 249:6 (2020), 974–988 https://rdcu.be/b6vMJ
94.	V. V. Karachik, B. Kh. Turmetov, “On solvability of some nonlocal boundary value problems for polyharmonic equation”, Kazakh Mathematical Journal, 19:1 (2019), 39–49 http://www.math.kz/media/journal/journal2019-07-2683070.pdf
95.	Zalyapin V.I., Karpeta T.V., Karachik V.V., Kharitonova E.V., “Valerii Leizerovich Dilman. K 70-letiyu so dnya rozhdeniya”, Vestnik Yuzhno-Uralskogo gosudarstvennogo universiteta. Seriya: Matematika. Mekhanika. Fizika., 11:4 (2019), 80–86
96.	V. V. Karachik, B. Kh. Turmetov, “On a class of Neumann type problems for polyharmonic equation”, AIP Conference Proceedings, 2172:030002 (2019), 1–6 https://aip.scitation.org/doi/abs/10.1063/1.5133491
97.	V. V. Karachik, “Ob odnom predstavlenii funktsii Grina zadachi Dirikhle dlya bigarmonicheskogo uravneniya v share”, Vestnik YuUrGU, Seriya «Matematika. Mekhanika. Fizika», 10:4 (2018), 13–22 https://vestnik.susu.ru/mmph/issue/view/517
98.	V. V. Karachik, B. Kh. Turmetov, “O razreshimosti nekotorykh nelokalnykh kraevykh zadach dlya bigarmonicheskogo uravneniya”, Byulleten Instituta matematiki, 2018, no. 4, 16–22 http://mib.mathinst.uz/en/2018.html
99.	V. V. Karachik, “O zadache tipa Robena dlya bigarmonicheskogo uravneniya v edinichnom share”, Problemy vychislitelnoi i prikladnoi matematiki, 2017, no. 1(7), 4-10
100.	V. V. Karachik, B. Kh. Turmetov, “Solvability of some Neumann-type boundary value problems for biharmonic equations”, Electronic Journal of Differential Equations, 2017:218 (2017), 1–17 https://ejde.math.txstate.edu/Volumes/2017/218/karachik.pdf
101.	V. V. Karachik, “Neumann type problem for polyharmonic equation in a ball”, Chelyab. Fiz.-Mat. Zh., 2:4 (2017), 420–429
102.	B. Kh. Turmetov, V. V. Karachik, “About one boundary value problem for the biharmonic equation”, AIP Conference Proceedings, 1789:040015 (2016), 040015-1–040015-6 http://aip.scitation.org/toc/apc/1789/1?expanded=1789
103.	L. D. Menikhes, V. V. Karachik, “On the regularizability conditions of integral equations”, Ob usloviyakh regulyarizuemosti integralnykh uravnenii, Vestnik YuUrGU. Seriya «Matematicheskoe modelirovanie i programmirovanie», 8:3 (2015), 142–148 http://mmp.vestnik.susu.ac.ru/pdf/v8n3st9.pdf
104.	V. V. Karachik, M. A. Sadybekov, B. T. Torebek, “Uniqueness of solutions to boundary-value problems for the biharmonic equation in a ball”, Electronic Journal of Differential Equations, 2015 (2015), 1–9
105.	V. V. Karachik, Metod normirovannykh sistem funktsii, Izdatelskii tsentr YuUrGU, Chelyabinsk, 2014 , 452 pp.
106.	V. V. Karachik, “Postroenie resheniya zadachi Dirikhle dlya poligarmonicheskogo uravneniya v share s polinomialnymi dannymi”, Sistemy kompyuternoi matematiki i ikh prilozheniya, Materialy XV mezhdunarodnoi nauchnoi konferentsii (Smolensk, 16-18 maya 2014 g.), Izdatelstvo SmolGU, 2014, 153–155
107.	V. V. Karachik, “On a nonclassical boundary value problem for the Helmholtz equation”, Vestn. Yuzhno-Ural. Gos. Un-ta. Ser. Matem. Mekh. Fiz., 6:3 (2014), 14–22
108.	V. V. Karachik, “Reshenie zadachi Dirikhle dlya poligarmonicheskogo uravneniya v share”, Vestnik Natsionalnogo issledovatelskogo yadernogo universiteta «MIFI», 3:6 (2014), 649–655
109.	V. V. Karachik, “Rows of Pascal's triangle modulo a prime”, Diskretn. Anal. Issled. Oper., 20:2 (2013), 26–46
110.	V. V. Karachik, “On the mean-value property for polyharmonic functions”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 6:3 (2013), 59–66
111.	V. V. Karachik, “On one generalized mean theorem for harmonic functions”, Vestn. Yuzhno-Ural. Gos. Un-ta. Ser. Matem. Mekh. Fiz., 5:1 (2013), 34–39
112.	V. V. Karachik, N. A. Antropova, “Construction of Polynomial Solutions to the Dirichlet Problem by Almansi Representation”, Journal of Mathematical Sciences, 188:3 (2013), 256–267
113.	V. V. Karachik, B. Kh. Turmetov, A. Bekaeva, “Solvability conditions of the Neumann boundary value problem for the biharmonic equation in the unit ball”, International Journal of Pure and Applied Mathematics, 81:3 (2012), 487–495
114.	V. V. Karachik, “Pascal’s triangle and $p$-latin matrices”, Vestn. Yuzhno-Ural. Gos. Un-ta. Ser. Matem. Mekh. Fiz., 2012, no. 7, 17–30
115.	V. V. Karachik, N. A. Antropova, “Construction of polynomial solutions to the Dirichlet problem for the biharmonic equation in a ball”, Vestn. Yuzhno-Ural. Gos. Un-ta. Ser. Matem. Mekh. Fiz., 2011, no. 5, 39–50
116.	V. V. Karachik, “Polynomial solutions to the systems of partial differential equations with constant coefficients”, Yokohama Math. J., 2000, no. 47, 121–142
117.	V. V. Karachik, “A generalized Neumann problem for harmonic functions in the half-space”, Differential Equations, 35:7 (1999), 949–955
118.	V. V. Karachik, “Continuity of polynomial solutions with respect to the coefficient of the higher derivative”, INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS, 28:9 (1997), 1229–1234
119.	V. V. Karachik, “P-Latin matrices and Pascal's triangle modulo a prime”, The Fibonacci Quarterly, 1996, no. 34(4), 362–372
120.	V. V. Karachik, “O pazpeshimosti odnoi zadachi s nopmalnymi ppoizvodnymi vysokogo popyadka na gpanitse”, DAN UzSSR, 1991, no. 6, 8–11
121.	V. V. Karachik, B. Kh. Turmetov, “Ob odnoi zadache dlya gapmonicheskogo upavneniya”, Izvestiya AN UzSSR, sep. fiz.-mat. nauk, 1990, no. 4, 17–21
122.	V. V. Karachik, G. Saidkapimova, “O pazpeshimosti zadachi Gupsa dlya lineinogo upavneniya Manzhepona s postoyannymi koeffitsientami”, DAN UzSSR, 1990, no. 9, 7–9
123.	V. V. Karachik, “Nekotopyi klass zadach dlya poligapmonicheskogo upavneniya v shape”, DAN UzSSR, 1989, no. 9, 7–8
124.	V. V. Karachik, B. A. Bondarenko, “Analogi formuly Eilera dlya obobschennoodnopodnykh funktsii”, DAN UzSSR, 1987, no. 5, 5–7
125.	V. V. Karachik, “Dinamika sistem n pap “khischnik-zheptva” svyazannykh po konkupentsii”, Izvestiya AN UzSSR, sepiya tekhn. nauk, 1977, no. 6, 3–9
126.	V. V. Karachik, Mat. Zametki (to appear)
127.	R. Zh. Aleev, V. L. Dil'man, A. D. Drozin, V. I. Zalyapin, V. V. Karachik, A. V. Keller, Yu. M. Kovalev, N. A. Manakova, G. A. Sviridyuk, E. V. Tabarintseva, “Leonid Menikhes (to the $65^{th}$ anniversary)”, Vestnik YuUrGU, 6:3 (2013), 136–140
128.	I. V. Bychkov, S. M. Voronin, O. N. Dementiev, V. L. Dilman, V. I. Zalyapin, D. A. Zakharyevich, D. B. Izergin, V. V. Karachik, A. Yu. Makovetskii, L. D. Menikhes, V. N. Pavlenko, M. V. Plekhanova, E. A. Sbrodova, S. V. Taskaev, V. I. Ukhobotov, Chelyab. Fiz.-Mat. Zh., 7:1 (2022), 5–10
129.	V. V. Karachik, N. V. Adukova, Teoriya funktsii kompleksnogo peremennogo, uchebnoe posobie dlya samostoyatelnoi raboty, Izdatelskii tsentr YuUrGU, Chelyabinsk, 2022 , 161 pp.
130.	V. V. Karachik, N. D. Ivanova, Mathematical analysis: uchebnoe posobie, Izdatelskii tsentr YuUrGU, Chelyabinsk, 2022 , 173 pp.
131.	Sh.A. Alimov, R.R. Ashurov, T.Sh. Kalmenov, B.E. Kanguzhin, V.V. Karachik, M.A. Sadybekov, A.M. Sarsenbi, D. Suragan, N.E. Tokmagambetov, B.T. Torebek, S.R. Umarov, V.E.Fedorov, “Batyrkhan Khudaibergenovich Turmetov (k 60-letiyu so dnya rozhdeniya)”, Chelyabinskii fiziko-matematicheskii zhurnal, 6:1 (2021), 5–9 http://cpmj.csu.ru/index.php/cpmj/issue/view/22
132.	Bragina A.A., Dilman V.L., Gerenshtein A.V., Goldenberg M.M., Karachik V.V., Kipnis M.M., Kungurtseva A.V., Makarov A.S., Martynova E.V., Matveeva L.V., Matveev S.V., Menikhes L.D., Strauss V.A., Sviridyuk G.A., Utkin P.B., Zagrebina S.A., Zalyapin V.I., Zamyshlyaeva A.A., “EVNIN ALEXANDER YUREVICH (SEPTEMBER 24, 1960 - NOVEMBER 19, 2020)”, Journal of Computational and Engineering Mathematics, 8:1 (2021), 74–78
133.	V. V. Karachik, N. D. Ivanova, Ordinary differential equations, uchebnoe posobie, Izdatelskii tsentr YuUrGU, Chelyabinsk, 2021 , 125 pp., angl.
134.	V. V. Karachik, Integraly Rimana i Lebega, Izdatelskii tsentr YuUrGU, Chelyabinsk, 2020 , 205 pp.
135.	V. V. Karachik, D. A. Komissarova, Matematicheskii analiz, Uchebnoe posobie, Chast II, Izdatelskii tsentr YuUrGU, Chelyabinsk, 2018 , 158 pp.
136.	V. L. Dil'man, V. I. Zalyapin, V. V. Karachik, L. D. Menikhes, “Mikhail Markovich Kipnis. To the seventy-five years anniversary”, Vestn. Yuzhno-Ural. Gos. Un-ta. Ser. Matem. Mekh. Fiz., 8:4 (2016), 70–75
137.	V. I. Zalyapin, V. V. Karachik, L. D. Menikhes, Ye. V. Kharitonova, “Boris Anisimovitch Bondarenko. To the 90-th anniversary”, Vestn. Yuzhno-Ural. Gos. Un-ta. Ser. Matem. Mekh. Fiz., 7:1 (2015), 65–67
138.	V. V. Karachik, L. D. Menikhes, Teoriya funktsii kompleksnogo peremennogo, Izdatelskii tsentr YuUrGU, Chelyabinsk, 2015 , 411 pp.
139.	V. I. Zalyapin, V. V. Karachik, L. R. Kim-Tyan, L. D. Menikhes, Yu. B. Rusak, “Boris Vladimirovich Loginov. K 75-letiyu so dnya rozhdeniya”, Vestnik YuUrGU. Seriya «Matematika. Mekhanika. Fizika», 6:4 (2014), 59–62
140.	V. V. Karachik, D. A. Komissarova, Matematicheskii analiz, uchebnoe posobie dlya samostoyatelnoi raboty, Izdatelskii tsentr YuUrGU, Chelyabinsk, 2014 , 87 pp.
141.	V. V. Karachik, Ryady Fure, 2-e izd., Izdatelskii tsentr YuUrGU, Chelyabinsk, 2014 , 126 pp.
142.	V. V. Karachik, Kurs matematicheskogo analiza, Izdatelskii tsentr YuUrGU, Chelyabinsk, 2009 , 682 pp.
143.	V. V. Karachik, Matematicheskii analiz, uchebnoe posobie dlya studentov inzhenerno-fizicheskikh i fiziko-matematicheskikh spetsialnostei universitetov, v. 2, Yuzhno-Uralskii gosudarstvennyi universitet, Chelyabinsk, 2008 , 267 pp.
144.	V. V. Karachik, Matematicheskii analiz, uchebnoe posobie dlya studentov inzhenerno-fizicheskikh i fiziko-matematicheskikh spetsialnostei universitetov, v. 1, Yuzhno-Uralskii gosudarstvennyi universitet, Chelyabinsk, 2008 , 154 pp.

Presentations in Math-Net.Ru

1.	On polynomial solutions of the Dirichlet problem for the polyharmonic equation in a ball V. V. Karachik International Conference on Differential Equations and Dynamical Systems July 7, 2014 15:00

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