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.