This article is cited in 1 paper

To the theory of boundary problems for elliptic equations with superposition operators in the boundary condition

A. K. Ratyni

Chair of Higher Mathematics, Ivanovo State University of Chemistry and Technology, Ivanovo, Russia

Abstract: We study the existence, uniqueness, and constant sign property of classical solutions to a nonlocal boundary value problem for a second-order elliptic equation in a bounded domain of the Euclidean space. Using the system of maps that define superposition operators, we construct some subset of the domain boundary and establish the connection between the solvability of the problem under consideration and the solvability of the boundary value equation on the constructed subset.

Keywords: nonlocal problem, subset of boundary, solvability of the boundary value equation.

UDC: 517.956

Received: 30.11.2011

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2013, 57:1, 44–53

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