Existence Results for Singular <i>p</i>-Biharmonic Problem with HARDY Potential and Critical Hardy-Sobolev Exponent

Abstract

In this article, we consider the singular p-biharmonic problem involving Hardy potential and critical Hardy–Sobolev exponent. Firstly, we study the existence of ground state solutions by using the minimization method on the associated Nehari manifold. Then, we investigate the least-energy sign-changing solutions by considering the Nehari nodal set. In both cases, the critical Sobolev exponent is of great importance as the solutions exists only if we are below the critical Sobolev exponent.

Keywords

• p-biharmonic problem
• Choquard equation
• ground state solution
• least-energy sign-changing solution