Multiplicity of nontrivial solutions for p‐Kirchhoff type equation with Neumann boundary conditions

Abstract

This paper is concerned with the multiplicity results to a class of ‐Kirchhoff type elliptic equation with the homogeneous Neumann boundary conditions by the abstract linking lemma due to Brézis 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. At the same time, this paper also gives a method to deal with ‐Laplacian, Kirchhoff equation, and some Kirchhoff type equation in a unified variational framework.