Multiple solutions for a Bibarmonic elliptic equation with critical Choquard type nonlinearity

Abstract

This article concerns the following Bibarmonic elliptic equation with critical growth where Ω ⊂ ℝ N is a smooth bounded domain , g(x) is a positive continuous function on is a real parameter, is the critical exponent in the sense of Hardy-Littlewood-Sobolev inequality. By combining the Nehari manifold and the variational methods, we prove the existence of k nontrivial solutions for this equation. Our results extend the results of Rani and Goyal in Topological Methods in Nonlinear Analysis 59 (2022), 221–260.