SOLVABILITY OF THE NONLINEAR BOUNDARY VALUE PROBLEMS USING THE GREEN FUNCTION

Abstract

The Green function has wide applications in the study of boundary value problems. In particular, the Green function is an important tool to show the existence and uniqueness of problems. In this paper, we study solvability of nonlinear boundary problems using the Green function. Differently from other authors, we reduce the problem to an operator equation for the right-hand side function. Consider this function in a specified bounded domain, we prove the contraction of the operator. This guarantees the existence and uniqueness of a solution of the problem.