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
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
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), 1015–1028https://rdcu.be/dKLLV
5.
M. Muratbekova, V. Karachik, B. Turmetov, “Bitsadze-Samarsky type problems with double involution”, Boundary Value Problems, 2024:86 (2024), 1-21
6.
V. V. Karachik, “Bigarmonicheskaya zadacha Neimana s dvoinoi involyutsiei”, Vestnik YuUrGU. Seriya «Matematika. Mekhanika. Fizika», 16:3 (2024), 18–26
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)
9.
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
V. V. Karachik, “Reshenie zadachi Rike–Neimana dlya poligarmonicheskogo uravneniya v share”, Vestnik YuUrGU. Seriya «Matematika. Mekhanika. Fizika», 15:1 (2023), 26–33
12.
V. V. Karachik, “The Green function of the Navier problem for the polyharmonic equation in a ball”, Journal of Mathematical Sciences, 269:2 (2023), 189–204https://rdcu.be/c5Sii
H. Yuan, V. Karachik, “Dirichlet and Neumann Boundary Value Problems for Dunkl Polyharmonic Equations”, Mathematics, 11:9 (2023), 2185https://www.mdpi.com/2227-7390/11/9/2185
15.
V. V. Karachik, “On Green function of the Dirichlet problem for polyharmonic equation in the ball”, Axioms, 12:6 (2023), 543https://www.mdpi.com/2075-1680/12/6/543
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), 1061–1074https://rdcu.be/dnV75
17.
V. V. Karachik, “On one integral representation of solutions of polyharmonic equation”, Lobachevskii Journal of Mathematics, 44:7 (2023), 2749–2756https://rdcu.be/dpI0k
18.
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
2022
19.
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
H. Yuan, V. Karachik, “Solutions of the generalized Dirichlet problem for the iterated slice Dirac equation”, Czechoslovak Mathematical Journal, 72:147 (2022), 523–539
21.
V. Karachik, B. Turmetov, H. Yuan, “Four Boundary Value Problems for a Nonlocal Biharmonic Equation in the Unit Ball”, Mathematics, 10:7 (2022), 1-21https://www.mdpi.com/2227-7390/10/7/1158#
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), 51–58https://vestnik.susu.ru/mmph/article/view/11942
23.
V. V. Karachik, “Solution to the Dirichlet Problem for the Polyharmonic Equation in the Ball”, Siberian Advances in Mathematics, 32:3 (2022), 197–210https://rdcu.be/cUSbv
24.
V. V. Karachik, “Reshenie zadachi Neimana dlya poligarmonicheskogo uravneniya v edinichnom share”, Sistemy kompyuternoi matematiki i ikh prilozheniya, 2022, no. 23, 241–246
25.
B. Turmetov, V. Karachik, “Construction of Eigenfunctions to One Nonlocal Second-Order Differential Operator with Double Involution”, Axioms, 11:10 (2022), 543https://www.mdpi.com/2075-1680/11/10/543
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
27.
V. V. Karachik, N. V. Adukova, Teoriya funktsii kompleksnogo peremennogo, uchebnoe posobie dlya samostoyatelnoi raboty, Izdatelskii tsentr YuUrGU, Chelyabinsk, 2022 , 161 pp.
28.
V. V. Karachik, N. D. Ivanova, Mathematical analysis: uchebnoe posobie, Izdatelskii tsentr YuUrGU, Chelyabinsk, 2022 , 173 pp.
2021
29.
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
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), 1276–1288http://link.springer.com/article/10.1134/S0965542521040059
32.
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, 75–90https://link.springer.com/chapter/10.1007/978-3-030-69292-6_5
33.
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, 060002https://aip.scitation.org/doi/abs/10.1063/5.0057206
34.
V. V. Karachik, “Dirichlet and Neumann boundary value problems for the polyharmonic equation in the unit ball”, Mathematics, 9:16 (2021), 1907
B. Turmetov, V. Karachik, M. Muratbekova, “On a boundary value problem for the biharmonic equation with multiple involution”, Mathematics, 9:17 (2021), 2020https://doi.org/10.3390/math9172020
V. V. Karachik, “The Green Function of the Dirichlet Problem for the Triharmonic Equation in the Ball”, Mathematical Notes, 107:1 (2020), 105–120
44.
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
45.
V. Karachik, B. Turmetov, “On solvability of some nonlocal boundary value problems for biharmonic equation”, Mathematica Slovaca, 70:2 (2020), 329–342
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
47.
V. V. Karachik, “Neumann type problems for the polyharmonic equation in ball”, Journal of Mathematical Sciences, 249:6 (2020), 974–988https://rdcu.be/b6vMJ
48.
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
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
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
53.
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
V. V. Karachik, “Solving a Problem of Robin Type for Biharmonic Equation”, Russian Mathematics, 62:2 (2018), 34–48https://rdcu.be/bqQ8z
58.
V. V. Karachik, “Riquier-Neumann Problem for the Polyharmonic Equation in a Ball”, Differential Equations, 54:5 (2018), 648–657
59.
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
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
2018
61.
V. V. Karachik, “Ob odnom predstavlenii funktsii Grina zadachi Dirikhle dlya bigarmonicheskogo uravneniya v share”, Vestnik YuUrGU, Seriya «Matematika. Mekhanika. Fizika», 10:4 (2018), 13–22https://vestnik.susu.ru/mmph/issue/view/517
62.
V. V. Karachik, B. Kh. Turmetov, “O razreshimosti nekotorykh nelokalnykh kraevykh zadach dlya bigarmonicheskogo uravneniya”, Byulleten Instituta matematiki, 2018, no. 4, 16–22http://mib.mathinst.uz/en/2018.html
63.
V. V. Karachik, D. A. Komissarova, Matematicheskii analiz, Uchebnoe posobie, Chast II, Izdatelskii tsentr YuUrGU, Chelyabinsk, 2018 , 158 pp.
2017
64.
V. V. Karachik, B. T. Torebek, “On the Dirichlet–Riquier Problem for Biharmonic Equations”, Mathematical Notes, 102:1 (2017), 31–42
65.
V. V. Karachik, “O zadache tipa Robena dlya bigarmonicheskogo uravneniya v edinichnom share”, Problemy vychislitelnoi i prikladnoi matematiki, 2017, no. 1(7), 4-10
66.
V. V. Karachik, “A Neumann-type problem for the biharmonic equation”, Siberian Advances in Mathematics, 27:2 (2017), 103–118
V. V. Karachik, “Integral identities on a sphere for normal derivatives of polyharmonic functions”, SIBERIAN ELECTRONIC MATHEMATICAL REPORTS, 14 (2017), 533–551
68.
V. V. Karachik, “Generalized Third Boundary Value Problem for the Biharmonic Equation”, Differential Equations, 53:6 (2017), 756–765
69.
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), 1–17https://ejde.math.txstate.edu/Volumes/2017/218/karachik.pdf
70.
V. V. Karachik, “Neumann type problem for polyharmonic equation in a ball”, Chelyab. Fiz.-Mat. Zh., 2:4 (2017), 420–429
2016
71.
H. Yuan, V. V. Karachik, “Representations of super-holomorphic functions and their applications”, Complex Variables and Elliptic Equations, 61:11 (2016), 1517–1532
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
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), 020118-1-020118-6http://dx.doi.org/10.1063/1.4959732
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
B. Kh. Turmetov, V. V. Karachik, “About one boundary value problem for the biharmonic equation”, AIP Conference Proceedings, 1789:040015 (2016), 040015-1–040015-6http://aip.scitation.org/toc/apc/1789/1?expanded=1789
2017
76.
V. V. Karachik, “A Neumann-type problem for the biharmonic equation”, Siberian Adv. Math., 27:2 (2017), 103–118
2016
77.
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
2015
78.
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
79.
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
80.
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), 142–148http://mmp.vestnik.susu.ac.ru/pdf/v8n3st9.pdf
81.
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
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
84.
V. V. Karachik, L. D. Menikhes, Teoriya funktsii kompleksnogo peremennogo, Izdatelskii tsentr YuUrGU, Chelyabinsk, 2015 , 411 pp.
2014
85.
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
86.
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
87.
V. V. Karachik, “On the Arithmetic Triangle Arising from the Solvability Conditions for the Neumann Problem”, Math. Notes, 96:2 (2014), 217–227
88.
V. V. Karachik, Metod normirovannykh sistem funktsii, Izdatelskii tsentr YuUrGU, Chelyabinsk, 2014 , 452 pp.
89.
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
90.
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
91.
V. V. Karachik, “Solvability Conditions for the Neumann Problem for the Homogeneous Polyharmonic Equation”, Differential Equations, 50:11 (2014), 1449–1456
92.
V. V. Karachik, “Reshenie zadachi Dirikhle dlya poligarmonicheskogo uravneniya v share”, Vestnik Natsionalnogo issledovatelskogo yadernogo universiteta «MIFI», 3:6 (2014), 649–655
93.
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
94.
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
95.
V. V. Karachik, D. A. Komissarova, Matematicheskii analiz, uchebnoe posobie dlya samostoyatelnoi raboty, Izdatelskii tsentr YuUrGU, Chelyabinsk, 2014 , 87 pp.
96.
V. V. Karachik, Ryady Fure, 2-e izd., Izdatelskii tsentr YuUrGU, Chelyabinsk, 2014 , 126 pp.
2013
97.
V. V. Karachik, “On some special polynomials and functions”, Sib. Èlektron. Mat. Izv., 10 (2013), 205–226
98.
V. V. Karachik, “Rows of Pascal's triangle modulo a prime”, Diskretn. Anal. Issled. Oper., 20:2 (2013), 26–46
99.
V. V. Karachik, “On the mean-value property for polyharmonic functions”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 6:3 (2013), 59–66
2014
100.
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
101.
V. V. Karachik, “On the mean value property for polyharmonic functions in the ball”, Siberian Advances in Mathematics, 24:3 (2014), 169–182
2013
102.
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
103.
V. V. Karachik, “On an arithmetical triangle”, Journal of Mathematical Sciences, 195:5 (2013), 665–675
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
105.
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
106.
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
2012
107.
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
108.
V. V. Karachik, “Method for constructing solutions of linear ordinary differential equations with constant coefficients”, Comput. Math. Math. Phys., 52:2 (2012), 219–234
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
111.
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
112.
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
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
2011
115.
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
116.
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
117.
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
118.
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
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
120.
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
2009
121.
V. V. Karachik, Kurs matematicheskogo analiza, Izdatelskii tsentr YuUrGU, Chelyabinsk, 2009 , 682 pp.
2008
122.
V. V. Karachik, “On an Expansion of Almansi Type”, Math. Notes, 83:3 (2008), 335–344
123.
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.
124.
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.
125.
V. V. Karachik, “On One Representation of Analytic Functions by Harmonic Functions”, Siberian Adv. Math., 18:2 (2008), 103–117
2004
126.
V. V. Karachik, “On some special polynomials”, Proceedings of American Mathematical Society, 132:4 (2004), 1049-1058
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
V. V. Karachik, “Polynomial Solutions to the Lamé Equations”, Siberian Adv. Math., 13:2 (2003), 66–79
2000
129.
V. V. Karachik, “Polynomial solutions to the systems of partial differential equations with constant coefficients”, Yokohama Math. J., 2000, no. 47, 121–142
1999
130.
V. V. Karachik, “A generalized Neumann problem for harmonic functions in the half-space”, Differential Equations, 35:7 (1999), 949–955
1998
131.
V. V. Karachik, “On one set of orthogonal harmonic polynomials”, Proceedings of American Mathematical Society, 126:12 (1998), 3513-3519
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
1996
134.
V. V. Karachik, “A problem with higher-order normal derivatives on the boundary for the Poisson equation”, Differential Equations, 32:3 (1996), 421–424
135.
V. V. Karachik, “P-Latin matrices and Pascal's triangle modulo a prime”, The Fibonacci Quarterly, 1996, no. 34(4), 362–372
1992
136.
V. V. Karachik, “O pazpeshimosti kpaevoi zadachi dlya upavneniya Gelmgoltsa s nopmalnymi ppoizvodnymi vysokogo popyadka na gpanitse”, Differentsialnye uravneniya, 28:5 (1992), 907–909
V. V. Karachik, “A problem for the polyharmonic equation in the sphere”, Siberian Mathematical Journal, 32:5 (1991), 767–774
139.
V. V. Karachik, “O pazpeshimosti odnoi zadachi s nopmalnymi ppoizvodnymi vysokogo popyadka na gpanitse”, DAN UzSSR, 1991, no. 6, 8–11
1990
140.
V. V. Karachik, B. Kh. Turmetov, “Ob odnoi zadache dlya gapmonicheskogo upavneniya”, Izvestiya AN UzSSR, sep. fiz.-mat. nauk, 1990, no. 4, 17–21
141.
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