Multiple nontrivial solutions for $p$-Laplacian equations with an asymmetric nonlinearity

Abstract

In this paper we study a nonlinear Dirichlet problem driven by the p-Laplacian and a right-hand side nonlinearity which exhibits an asymmetric behavior near $+ \infty$ and $- \infty$. Using variational techniques based on the mountain pass theorem and the second deformation theorem, we prove the existence of at least two nontrivial $C^1$- solutions, one of which is strictly positive.