Kh.A. Khachatryan, H.S. Petrosyan, M.H. Avetisyan. Solvability issues for a class of convolution type nonlinear integral equations in $\mathbb {R}^n$

We study a class of nonlinear multidimensional integral equations of convolution type. This class of equations is directly applied in the $p$-adic theory of open-closed strings. We prove the existence of an $n$-parametric family of nontrivial continuous bounded solutions and establish certain properties of the constructed solutions: monotonicity in each argument, limit relations, and integral asymptotics. The solutions are used to study a nonlinear problem for the multidimensional heat equation. At the end of the paper we give example of such equations, which are of independent theoretical and practical interest.

Keywords: nontrivial solution, monotonicity, $p$-adic theory, limit, successive approximations.

The paper was received by the Editorial Office on June 26, 2018.

Funding Agency: This work was supported by the Science Committee of the Ministry of Education and Science of Armenia (project no. SCS 16YR-1A002).

Khachatur Aghavardovich Khachatryan, Dr. Phys.-Math. Sci., Institute of Mathematics, National Academy of Sciences of Armenia, 0019, Yerevan, Republic of Armenia, e-mail:,

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

Metaksya Hovnanovna Avetisyan, graduate student, Yerevan State University, 0025, Yerevan, Republic of Armenia, e-mail:


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