$p$-biharmonic equation with Hardy–Sobolev exponent and without the Ambrosetti–Rabinowitz condition

Abstract

This paper is concerned with the existence and multiplicity to $p$-biharmonic equation with Sobolev–Hardy term under Dirichlet boundary conditions and Navier boundary conditions, respectively. We focus on the case of the nonlinear terms without the Ambrosetti–Rabinowitz conditions. Our method is based on the variational method.

Keywords

• variational methods
• $p$-biharmonic equation
• sobolev–hardy inequality
• fountain theorem