To the theory of boundary-value problems for elliptic equations with superposition operators in the boundary condition. I

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.