Solvability of a class of integro-differential equations with Laplace and bi-Laplace operators

Vitali Vougalter; Vitaly Volpert

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arXiv · 2603.07804

Solvability of a class of integro-differential equations with Laplace and bi-Laplace operators

Vitali Vougalter·Vitaly Volpert

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Abstract

The work deals with the studies of the existence of solutions of an integro-differential equation in the situation of the difference of the standard Laplacian and the bi-Laplacian in the diffusion term. The proof of the existence of solutions relies on a fixed point technique. We use the solvability conditions for the non-Fredholm elliptic operators in unbounded domains.

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Vitali Vougalter, Vitaly Volpert. 2026-03-08. Solvability of a class of integro-differential equations with Laplace and bi-Laplace operators. https://arxiv.org/abs/2603.07804

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