Solvability conditions for three-point problem for a partial differential equation in two-dimensional cylinder

Abstract

The paper deals with the investigation of a three-point problem for a partial differential equation in a two-dimensional domain. We estab\-lish sufficient conditions for the existence of a solution to this problem and sufficient and necessary conditions for the uniqueness of the solution in the corresponding weighted Sobolev spaces (Abel spaces). A similar problem for an equation in several spatial variables is ill-posed in the sense of Hadamard; its solvability is connected with the problem of small denominators, which arises in the construction of the solution. In the case of a single spatial variable we estimate the corresponding denominators by constants and show that the problem is well-posed in the sense of Hadamard in the Abel spaces.