Extremal solutions and strong relaxation for nonlinear multivalued systems with maximal monotone terms

Abstract

We consider differential systems in R^N driven by a nonlinear nonhomogeneous second order differential operator, a maximal monotone term and a multivalued perturbation F(t,u,u'). For periodic systems we prove the existence of extremal trajectories, that is solutions of the system in which F(t,u,u') is replaced by extF(t,u,u') (= the extreme points of F(t,u,u')). For Dirichlet systems we show that the extremal trajectories approximate the solutions of the "convex" problem in the C^1(T,R^N)-norm (strong relaxation).