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).
Papageorgiou, N.S., Vetro, C., Vetro, F. (2018). Extremal solutions and strong relaxation for nonlinear multivalued systems with maximal monotone terms. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 461(1), 401-421 [10.1016/j.jmaa.2018.01.009].
Extremal solutions and strong relaxation for nonlinear multivalued systems with maximal monotone terms
Vetro, Calogero
;Vetro, Francesca
2018-01-01
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).
| File | Dimensione | Formato | |
|---|---|---|---|
|
2018_JMAA_PapageorgiouVetroVetro.pdf
Solo gestori archvio
Descrizione: Articolo principale
Dimensione
434.88 kB
Formato
Adobe PDF
|
434.88 kB | Adobe PDF | Visualizza/Apri Richiedi una copia |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
