Pairs of positive solutions for resonant singular equations with the p-Laplacian

Abstract

We consider a nonlinear elliptic equation driven by the Dirichlet p-Laplacian with a singular term and a (p-1)-linear perturbation which is resonant at $+\infty$ with respect to the principal eigenvalue. Using variational tools, together with suitable truncation and comparison techniques, we show the existence of at least two positive smooth solutions.

Keywords

• Singular reaction
• resonance
• regularity
• positive solutions
• maximum principle
• mountain pass theorem