Existence and relaxation results for second order multivalued systems
type: Item
instance of: scholarly article
title: Existence and relaxation results for second order multivalued systems
zbMATH Open document ID: 1476.34066
author: Nikolaos S. Papageorgiou
author: Calogero Vetro
published in: Acta Applicandae Mathematicae
publication date: 2021-07-30T00:00:00Z
review text: The authors study a second order multivalued boundary value problem of the form \[ \begin{cases} a(u'(t))'\in A(u(t))+F(t,u(t),u'(t))& \text{for a.\,a.\,}t\in T=[0,b]\\ u\in \text{BC},& \end{cases} \] where BC stands for Dirichlet, Neumann, periodic or mixed boundary conditions. The nonlinear system above is driven by a general nonhomogeneous differential operator with a reaction in which one has the combined effects of a maximal monotone term \(A(x)\) and of a multivalued perturbation \(F(t,x,y)\) which can be convex or nonconvex valued. The authors consider the cases where \(D(A)\neq \mathbb{R}^N\) and \(D(A)=\mathbb{R}^N\) and prove existence and relaxation theorems. Applications to differential variational inequalities and control systems are also discussed.
reviewed by: Patrick Winkert
Mathematics Subject Classification ID: 34A60
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 47H06
zbMATH DE Number: 7376840
zbMATH Keywords: maximal monotone map
zbMATH Keywords: convex and nonconvex problems
zbMATH Keywords: continuous and measurable selections
zbMATH Keywords: relaxation
zbMATH Keywords: optimal control
MaRDI profile type: Publication
full work available at URL: s10440-021-00410-9
OpenAlex ID: W3158200331
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DOI: 10.1007/S10440-021-00410-9
description: scientific article; zbMATH DE number 7376840