Kh.A. Khachatryan, H.S. Petrosyan, M.H. Avetisyan. Existence and uniqueness theorems for one system of integral equations with two nonlinearities ... P. 202-218

We consider a system of integral equations on the positive semiaxis with two monotone nonlinearities. With various particular representations of matrix kernels and nonlinearities, this system arises in many branches of mathematical physics. A constructive existence theorem for a non-negative, non-trivial and bounded solution is proved. We also study the asymptotic behavior of the solution at infinity. Under additional restrictions on the nonlinearities and matrix kernels, a uniqueness theorem for a solution, in a certain class of bounded vector functions, is proved. At the end, specific examples of matrix kernels and nonlinearities are given.

Keywords: matrix kernel, nonlinearity, bounded solution, monotonicity, convergence, limit relation

Received January 9, 2023

Revised January 23, 2023

Accepted January 30, 2023

Funding Agency: The work of the first and second authors was supported by the Russian Science Foundation (19-11-00223).

Khachatur Aghavardovich Khachatryan, Dr. Phys.-Math. Sci., Prof., Yerevan State University, 0025 Yerevan, Republic of Armenia; Lomonosov Moscow State University, Moscow, 119991, Russia, e-mail:,

Haykanush Samvelovna Petrosyan, Cand. Sci. (Phys.-Math.), Armenian National Agrarian University, 0009, Yerevan, Republic of Armenia; Lomonosov Moscow State University, Moscow, 119991, Russia, e-mail:

Metaksya Hovnanovna Avetisyan, Cand. Sci. (Phys.-Math.), Armenian National Agrarian University, 0009, Yerevan, Republic of Armenia; e-mail:


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Cite this article as: Kh.A. Khachatryan, H.S. Petrosyan, M.H. Avetisyan. Existence and uniqueness theorems for one system of integral equations with two nonlinearities, Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2023, vol. 29, no. 1, pp. 202–218.