Existece and multiplicity results for nonlinear critical Neumann problem on compact manifolds

TL;DR

This paper investigates the existence and multiplicity of solutions for a nonlinear Neumann boundary value problem involving the p-Laplacian and critical Sobolev exponents on compact Riemannian manifolds.

Contribution

It provides new existence and multiplicity results for nonlinear Neumann problems with critical exponents on compact manifolds.

Findings

Existence of solutions under certain geometric conditions

Multiple solutions established using variational methods

Results extend previous work to p-Laplacian and manifold settings

Abstract

we study on compact Riemannian manifolds with boundary, the problems of existence and multiplicity of solutions to a Neumann problem involving the p-Laplacian operator and critical Sobolev exponents.