A. Kh. Khachatryan, Kh. A. Khachatryan, “On the Solvability of Some Nonlinear Integral Equations in Problems of Epidemic Spread”, Mathematical physics and applications, Collected papers. In commemoration of the 95th anniversary of Academician Vasilii Sergeevich Vladimirov, Trudy Mat. Inst. Steklova, 306, Steklov Math. Inst. RAS, Moscow, 2019, 287–303; Proc. Steklov Inst. Math., 306 (2019), 271

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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2019, Volume 306, Pages 287–303
DOI: https://doi.org/10.4213/tm4006 (Mi tm4006)

This article is cited in 20 scientific papers (total in 20 papers)

On the Solvability of Some Nonlinear Integral Equations in Problems of Epidemic Spread

A. Kh. Khachatryan^a, Kh. A. Khachatryan^b

^a Armenian National Agrarian University, Teryan 74, Yerevan, 0009, Republic of Armenia
^b Institute of Mathematics of National Academy of Sciences of the Republic of Armenia, Marshal Baghramian ave. 24/5, Yerevan, 0019, Republic of Armenia

Full-text PDF (237 kB) Citations (20)

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DOI: https://doi.org/10.4213/tm4006

Abstract: We study some classes of convolution-type nonlinear integral equations that are directly related to the problems of geographic spread of epidemic diseases. Under various constraints on the nonlinearity and the kernel of the equation, we prove existence theorems for monotonic and bounded solutions. We also present specific examples of application of these equations.

Keywords: epidemic, iterations, monotonicity, nonlinearity, bounded solution.

Funding agency	Grant number
State Committee on Science of the Ministry of Education and Science of the Republic of Armenia	SCS 18T-1A004
The research was supported by the State Committee of Science of the Ministry of Education and Science of the Republic of Armenia, project no. SCS 18T-1A004.

Received: June 11, 2018
Revised: July 4, 2018
Accepted: June 24, 2019

English version:
Proceedings of the Steklov Institute of Mathematics, 2019, Volume 306, Pages 271–287
DOI: https://doi.org/10.1134/S0081543819050225

Bibliographic databases:

Document Type: Article

UDC: 517.968.43+517.958:57

Language: Russian

Citation: A. Kh. Khachatryan, Kh. A. Khachatryan, “On the Solvability of Some Nonlinear Integral Equations in Problems of Epidemic Spread”, Mathematical physics and applications, Collected papers. In commemoration of the 95th anniversary of Academician Vasilii Sergeevich Vladimirov, Trudy Mat. Inst. Steklova, 306, Steklov Math. Inst. RAS, Moscow, 2019, 287–303; Proc. Steklov Inst. Math., 306 (2019), 271–287

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https://doi.org/10.4213/tm4006

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This publication is cited in the following 20 articles:

Kh. A. Khachatryan, H. S. Petrosyan, “On qualitative properties of the solution of a boundary value problem for a system of nonlinear integral equations”, Theoret. and Math. Phys., 218:1 (2024), 145–162
Kh. A. Khachatryan, H. S. Petrosyan, “An iterative method for solving one class of non-linear integral equations with Nemytskii operator on the positive semi-axis”, Izv. Math., 88:4 (2024), 760–793
Kh. A. Khachatryan, H. S. Petrosyan, “Asymptotic Behavior of the Solution for One Class of Nonlinear Integral Equations of Hammerstein Type on the Whole Axis”, J Math Sci, 282:2 (2024), 292
Kh. A. Khachatryan, H. S. Petrosyan, A. R. Hakobyan, “On solvability of one class of integral equations on whole line with monotonic and convex nonlinearity”, J. Math. Sci., 271:5 (2023), 610
A. Kh. Khachatryan, Kh. A. Khachatryan, “On qualitative properties of a solution of one class singular integral equations on the whole line with odd nonlinearity”, J. Math. Sci., 271:5 (2023), 597
Kh. A. Khachatryan, A. S. Petrosyan, “Asimptoticheskoe povedenie resheniya dlya odnogo klassa nelineinykh integralnykh uravnenii tipa Gammershteina na vsei pryamoi”, SMFN, 68, no. 2, Rossiiskii universitet druzhby narodov, M., 2022, 376–391
Kh. A. Khachatryan, H. S. Petrosyan, “On summable solutions of a class of nonlinear integral equations on the whole line”, Izv. Math., 86:5 (2022), 980–991
N. R. Ikonomov, S. P. Suetin, “Struktura nattollovskogo razbieniya dlya nekotorogo klassa chetyrekhlistnykh rimanovykh poverkhnostei”, Tr. MMO, 83, no. 1, MTsNMO, M., 2022, 37–61
Kh. A. Khachatryan, H. S. Petrosyan, “On the solvability of a class of nonlinear Urysohn integral equations on the positive half-line”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 36 (2021), 57–68
Kh. A. Khachatryan, H. S. Petrosyan, “Alternating bounded solutions of a class of nonlinear two-dimensional convolution-type integral equations”, Trans. Moscow Math. Soc., 82 (2021), 259–271
Kh. A. Khachatryan, H. S. Petrosyan, “Integral Equations on the Whole Line with Monotone Nonlinearity and Difference Kernel”, J Math Sci, 255:6 (2021), 790
A. Kh. Khachatryan, Springer Proceedings in Mathematics & Statistics, 358, Operator Theory and Harmonic Analysis, 2021, 253
A. Kh. Khachatryan, Kh. A. Khachatryan, H. S. Petrosyan, “Solvability of Two-Dimensional Integral Equations with Monotone Nonlinearity”, J Math Sci, 257:5 (2021), 720
Kh. A. Khachatryan, H. S. Petrosyan, “On solvability of a class of multidimensional integral equations in the mathematical theory of geographic distribution of an epidemic”, J. Contemp. Math. Anal.-Armen. Aca., 56:3 (2021), 143–157
A. Kh. Khachatryan, Kh. A. Khachatryan, “On solvability of one infinite system of nonlinear functional equations in the theory of epidemics”, Eurasian Math. J., 11:2 (2020), 52–64
M. H. Avetisyan, “On solvability of a nonlinear discrete system in the spread theory of infection”, Uch. zapiski EGU, ser. Fizika i Matematika, 54:2 (2020), 87–95
T. K. Yuldashev, S. K. Zarifzoda, “New type super singular integro-differential equation and its conjugate equation”, Lobachevskii J. Math., 41:6, SI (2020), 1123–1130
T. K. Yuldashev, S. K. Zarifzoda, “Mellin transform and integro-differential equations with logarithmic singularity in the kernel”, Lobachevskii J. Math., 41:9, SI (2020), 1910–1917
Kh. A. Khachatryan, A. Zh. Narimanyan, A. Kh. Khachatryan, “On mathematical modelling of temporal spatial spread of epidemics”, Math. Model. Nat. Phenom., 15 (2020), 6
Kh. A. Khachatryan, “Solvability of some nonlinear boundary value problems for singular integral equations of convolution type”, Trans. Moscow Math. Soc., 81:1 (2020), 1–31

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Труды Математического института имени В. А. Стеклова

Proceedings of the Steklov Institute of Mathematics

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