$p$-Kirchhoff type equation with Neumann boundary conditions

TL;DR

This paper investigates multiple solutions for a class of p-Kirchhoff elliptic equations with Neumann boundary conditions, extending known results in both subcritical and critical cases using an abstract linking lemma.

Contribution

It provides new multiplicity results for p-Kirchhoff equations with Neumann boundary conditions, covering subcritical and critical cases with a novel application of an abstract linking lemma.

Findings

Established multiplicity results in subcritical case

Extended results to critical case

Enhanced understanding of Kirchhoff equations with Neumann conditions

Abstract

This paper is concerned with the multiplicity results to a class of $p$-Kirchhoff type elliptic equation with the homogeneous Neumann boundary conditions by an abstract linking lemma due to Br\'{e}zis and Nirenberg. We obtain the twofold results in subcritical and critical cases, which is a meaningful addition and completeness to the known results about Kirchhoff equation.