Boundary Value Problem for the φ-Laplacian with Operator Right-Hand Side

Abstract

Abstract—General sufficient conditions for the existence of a solution of a boundary value problem for the φ-Laplacian with functional boundary conditions are obtained. As a consequence of this result, natural restrictions on the lower and upper functions are obtained under which there exists a solution of a periodic boundary value problem for the φ-Laplacian. Several applications of this results to the proof of the existence of solutions of boundary value problems for higher-order equations are given.