A study of biharmonic equation involving nonlocal terms and critical Sobolev exponent

TL;DR

This paper explores the existence and non-existence of solutions to a biharmonic equation with nonlocal terms and critical Sobolev exponent, using variational methods and Pohozaev identities.

Contribution

It provides new results on solution existence and non-existence for complex biharmonic equations with nonlocal and critical exponent features.

Findings

Non-existence of non-trivial solutions via Pohozaev identity

Existence of ground state solutions through minimization on Nehari manifold

Conditions under which solutions do or do not exist

Abstract

In this paper, we investigate the existence of ground state solutions and non-existence of non-trivial weak solution of biharmonic equation with some nonlocal terms and critical Sobolev exponent. Firstly, we prove the non-existence by establishing Pohozaev type of identity. Next, we study the existence of ground state solutions by using the minimization method on the associated Nehari manifold.