Geodesic
Solvability of one nonlocal Dirichlet problem for the Poisson equation
Novi Sad Journal of Mathematics, Tome 50 (2020) no. 1.

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In this paper the solvability of a new class of nonlocal boundary value problems for the Poisson equation is studied. These problems are a generalization of the classical Dirichlet boundary value problem. Existence and uniqueness theorems for the considering problem are proved. An integral representation of the solution is established. The notion of the Green's function for the problem under consideration is introduced and an explicit form of this function is constructed. The corresponding spectral issues are also studied, namely eigenfunctions and eigenvalues of the considered problem are found. For one particular case of the problem the completeness of the system of eigenfunctions is proved.
Publié le :
DOI : 10.30755/NSJOM.08942
Classification : 31B05, 35A09, 35C15
Keywords: nonlocal boundary value problem, Poisson equation, orthogonal matrix, involution, Dirichlet problem, Green's function, eigenfunctions, eigenvalues 
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     author = {Valery  Karachik and Batirkhan Turmetov},
     title = {Solvability of one nonlocal {Dirichlet} problem for the {Poisson} equation},
     journal = {Novi Sad Journal of Mathematics},
     pages = {67 - 88},
     publisher = {mathdoc},
     volume = {50},
     number = {1},
     year = {2020},
     doi = {10.30755/NSJOM.08942},
     url = {http://geodesic.mathdoc.fr/articles/10.30755/NSJOM.08942/}
}
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Valery  Karachik; Batirkhan Turmetov. Solvability of one nonlocal Dirichlet problem for the Poisson equation. Novi Sad Journal of Mathematics, Tome 50 (2020) no. 1. doi : 10.30755/NSJOM.08942. http://geodesic.mathdoc.fr/articles/10.30755/NSJOM.08942/

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