Differential equations

Existence of the solution for boundary value problem

S. V. Repjevskij

Chelyabinsk State University

Abstract: This article concerns the boundary value problem for the second-order elliptical equation in a bounded domain. The coefficient of the desired function is non-positive all over domain, but in the small neighborhood of an interior point. The question is, under what coefficient’s contingencies in this small neighborhood of an interior point statements claiming existing and uniqueness of solution the boundary value problem remain true.

Keywords: elliptical equation, boundary value problem.