The existence of solutions for quasilinear elliptic problems with combined critical Sobolev–Hardy terms☆

Abstract In this paper, we investigate the quasilinear elliptic equations with Dirichlet boundary conditions and combined critical Sobolev–Hardy terms on bounded smooth domains Ω ⊂ R N ( N ⩾ 3 ) , and prove the existence and multiplicity of solutions by employing Ekelandʼs variational principle.