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

Calogero Vetro, Francesca Vetro, Nikolaos S. Papageorgiou

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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).
Original languageEnglish
Pages (from-to)401-421
Number of pages21
JournalJournal of Mathematical Analysis and Applications
Volume461
Publication statusPublished - 2018

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All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

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