6533b82cfe1ef96bd1290036

RESEARCH PRODUCT

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

Francesca VetroCalogero VetroNikolaos S. Papageorgiou

subject

Differential inclusionPure mathematicsApplied Mathematics010102 general mathematicsRegular polygonMaximal monotone mapAnalysiPerturbation (astronomy)Bang-bang controlExtremal trajectorieDifferential operator01 natural sciencesDirichlet distribution010101 applied mathematicsNonlinear systemsymbols.namesakeMonotone polygonSettore MAT/05 - Analisi MatematicaNorm (mathematics)symbols0101 mathematicsExtreme pointStrong relaxationAnalysisMathematics

description

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 ext F ( 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).

yearjournalcountryeditionlanguage
2018-05-01Journal of Mathematical Analysis and Applications
https://doi.org/10.1016/j.jmaa.2018.01.009