Existence and Multiplicity of solutions for Kirchhoff type equations in Physical Education

TL;DR

This paper proves the existence of solutions for Kirchhoff type equations using critical point theory, specifically the Mountain Pass Theorem, without relying on the Palais-Smale condition.

Contribution

It introduces a novel application of the Mountain Pass Theorem to Kirchhoff equations, establishing solution existence without the (PS) condition.

Findings

Existence of solutions for Kirchhoff equations proven.

Application of Mountain Pass Theorem without (PS) condition.

Advances in mathematical methods for nonlinear PDEs.

Abstract

The fact that potentially skilled, but biologically later-maturing athletes are less likely to be selected into talent development programmes can represent a failure of Talent Identification in sports. In this article, we prove the existence of solutions for Kirchhoff type equations with Dirichlet boundaryvalue condition. We use the Mountain Pass Theorem in critical point theory, without the (PS) condition.