Existence and multiplicity of solutions for $p$-Kirchhoff-type Neumann problems

Abstract

We establish, based on variational methods, existence theorems for a p-Kirchhoff-type Neumann problem under the Landesman-Lazer type condition and under the local coercive condition. In addition, multiple solutions for a p-Kirchhoff-type Neumann problem are established using a known three-critical-point theorem proposed by H. Brezis and L. Nirenberg.