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).
|Number of pages||21|
|Journal||Journal of Mathematical Analysis and Applications|
|Publication status||Published - 2018|
All Science Journal Classification (ASJC) codes
- Applied Mathematics
Vetro, C., Vetro, F., & Papageorgiou, N. S. (2018). Extremal solutions and strong relaxation for nonlinear multivalued systems with maximal monotone terms. Journal of Mathematical Analysis and Applications, 461, 401-421.