Multiplicity of positive solutions for a critical quasilinear Neumann problem

TL;DR

This paper proves that there are multiple positive solutions to a quasilinear Neumann boundary value problem involving critical exponents, in expanding spherical domains and hemispheres.

Contribution

It demonstrates the existence of multiple positive solutions for a critical quasilinear Neumann problem in specific geometric domains.

Findings

Multiple positive solutions are established for the problem.

Solutions exist in expanding balls and hemispheres.

The problem involves critical boundary exponents.

Abstract

We establish the multiplicity of positive solutions to a quasilinear Neumann problem in expanding balls and hemispheres with critical exponent in the boundary condition.