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

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