Existence of multiple solutions for quasi-linear degenerate elliptic equations

TL;DR

This paper investigates a class of quasi-linear degenerate elliptic equations related to manifolds with corner singularities, demonstrating the existence of infinitely many solutions using variational methods.

Contribution

It establishes the existence of infinitely many solutions for these equations, a novel result in the context of degenerate elliptic problems with corner singularities.

Findings

Proved existence of infinitely many solutions.

Applied variational methods to degenerate elliptic equations.

Linked degenerate operators to manifold singularities.

Abstract

The present paper is concerned a class of quasi-linear elliptic degenerate equations. The degenerate operator comes from the analysis of manifolds with corner singularity. Variational methods are applied to verify the existence of infinity many solutions for the problems.