Geodesic
Solvability issues for a class of convolution type nonlinear integral equations in $\mathbb {R}^n$
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 24 (2018) no. 3, pp. 247-262

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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. 
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     author = {Kh. A. Khachatryan and H. S. Petrosyan and M. H. Avetisyan},
     title = {Solvability issues for a class of convolution type nonlinear integral equations in $\mathbb {R}^n$},
     journal = {Trudy Instituta matematiki i mehaniki},
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Kh. A. Khachatryan; H. S. Petrosyan; M. H. Avetisyan. Solvability issues for a class of convolution type nonlinear integral equations in $\mathbb {R}^n$. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 24 (2018) no. 3, pp. 247-262. http://geodesic.mathdoc.fr/item/TIMM_2018_24_3_a21/