A critical point theorem on a closed ball and some applications to boundary value problems

TL;DR

This paper establishes a critical point theorem on a closed ball for a difference of convex functionals and explores its applications to boundary value problems, providing new tools for solving nonlinear differential equations.

Contribution

It introduces a novel critical point theorem applicable to convex functionals on closed balls and demonstrates its usefulness in boundary value problem applications.

Findings

Proves existence of critical points under new conditions

Establishes multiplicity results for solutions

Provides applications to boundary value problems

Abstract

We consider a functional being a difference of two differentiable convex functionals on a closed ball. Existence and multiplicity of critical points is investigated. Some applications are given.