Solvability of nonlocal Dirichlet problem for generalized Helmholtz equation in a unit ball

Batirkhan Turmetov, Valery V. Karachik

2022

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DOI 10.1080/17476933.2022.2040021
Data confidence 70 medium
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Abstract

In this paper, we study the solvability of a new class of nonlocal boundary value problems for the generalized Helmholtz equation in the unit ball. These problems are a generalization of the classical Dirichlet boundary value problem to the Helmholtz equation. For the considered problems, existence and uniqueness theorems are proved. Integral representation of solutions is established. Corresponding spectral questions are also investigated, namely, eigenfunctions and eigenvalues of the problem are found.