Multiple positive solutions for quasilinear elliptic problems with combined critical Sobolev–Hardy terms

Abstract

Abstract In this paper, we investigate the quasilinear elliptic equations involving multiple critical Sobolev–Hardy terms with Dirichlet boundary conditions on bounded smooth domains Ω⊂RN $\varOmega \subset R^{N}$ ( N≥3 ${N \ge 3} $), and prove the multiplicity of positive solutions by employing Ekeland’s variational principle and the maximum principle.

Keywords

• Quasilinear elliptic equation
• Sobolev–Hardy term
• Positive solution
• Ekeland’s variational principle