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On solvability of some nonlocal boundary value problems for biharmonic equation

Valery Karachik and Batirkhan Turmetov
From the journal Mathematica Slovaca

Abstract

In this paper a new class of well-posed boundary value problems for the biharmonic equation is studied. The considered problems are nonlocal boundary value problems of Bitsadze- -Samarskii type. These problems are solved by reducing them to Dirichlet and Neumann type problems. Theorems on existence and uniqueness of the solution are proved and exact solvability conditions of the considered problems are found. In addition, the integral representations of solutions are obtained.

  1. (Communicated by Giuseppe Di Fazio )

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Received: 2018-09-23
Accepted: 2019-09-24
Published Online: 2020-03-10
Published in Print: 2020-04-28

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