On a Dirichlet problem with $p$-Laplacian and asymmetric nonlinearity

Abstract

The existence of at least two nonnegative smooth solutions to a homogeneous Dirichlet problem with $p$-Laplacian and reaction ($p$–1)-linear, but asymmetric, at ±$\infty$ is investigated through variational and truncation techniques. The case $p=2$ is separately examined, obtaining a third nontrivial smooth solution via Morse’s theory.