The periodic Ambrosetti-Prodi problem for nonlinear perturbations of the p-Laplacian

Abstract

We prove an Ambrosetti-Prodi-type result for the periodic solutions of equation ${\left(|u^{\prime }{|}^{p-2}{u}^{\prime })\right)}^{\prime }+f(u)u^{\prime }+g(x,u)=t,$ when $f$ is arbitrary and $g(x,u)\to +\infty$ or $g(x,u)\to -\infty$ when $|u|\to \infty .$ The proof uses upper and lower solutions and Leray-Schauder degree.