Solvability of nonlocal Dirichlet problem for generalized Helmholtz equation in a unit ball
Turmetov B.K. Karachik V.V.
2023Taylor and Francis Ltd.
Complex Variables and Elliptic Equations
2023#68Issue 71204 - 1218 pp.
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.
34K06 , 35J05 , 35J25 , Dirichlet problem , eigenfunction , Helmholtz equation , involution , Nonlocal boundary value problem , orthogonal matrix
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Department of Mathematics, Khoja Akhmet Yassawi International Kazakh-Turkish University, Turkistan, Kazakhstan
Department of Mathematical Analysis, South Ural State University, Chelyabinsk, Russian Federation
Department of Mathematics
Department of Mathematical Analysis
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