Nonlinear systems with Hartman-type perturbations

Abstract

We consider a nonlinear Lienard-type system driven by a nonlinear, nonhomogeneous differential operator and a maximal monotone map. On the Carathéodory perturbation we do not impose any global growth condition. Instead we employ a Hartman-type hypotheses. Using tools from fixed point theory and the theory of operators of monotone type, we prove two existence theorems.