Geodesic
Existence and uniqueness theorems for one system of integral equations with two nonlinearities
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 29 (2023) no. 1, pp. 202-218

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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.
Mots-clés : matrix kernel, convergence, limit relation.
Keywords: nonlinearity, bounded solution, monotonicity 
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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 mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 29 (2023) no. 1, pp. 202-218. http://geodesic.mathdoc.fr/item/TIMM_2023_29_1_a15/