Existence and Relaxation Results for Second Order Multivalued Systems

We consider nonlinear systems driven by a general nonhomogeneous differential operator with various types of boundary conditions and with a reaction in which we have the combined effects of a maximal monotone term A ( x ) and of a multivalued perturbation F ( t , x , y ) which can be convex or nonco...

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Bibliographic Details
Published in:Acta applicandae mathematicae Vol. 173; no. 1
Main Authors: Papageorgiou, Nikolaos S., Vetro, Calogero
Format: Journal Article
Language:English
Published: Dordrecht Springer Netherlands 01.06.2021
Springer Nature B.V
Subjects:
Applications of Mathematics
Banach spaces
Boundary conditions
Calculus of Variations and Optimal Control; Optimization
Computational Mathematics and Numerical Analysis
Differential equations
Eigenvalues
Existence theorems
Hypotheses
Mathematics
Mathematics and Statistics
Nonlinear systems
Operators (mathematics)
Partial Differential Equations
Perturbation
Probability Theory and Stochastic Processes
Relaxation
34B15
34C25
Optimal control
Convex and nonconvex problems
Continuous and measurable selections
Maximal monotone map
47H06
ISSN:0167-8019, 1572-9036
Online Access:Get full text
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Summary:We consider nonlinear systems driven by a general nonhomogeneous differential operator with various types of boundary conditions and with a reaction in which we have 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. We consider the cases where D ( A ) ≠ R N and D ( A ) = R N and prove existence and relaxation theorems. Applications to differential variational inequalities and control systems are discussed.
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ISSN:0167-8019
1572-9036
DOI:10.1007/s10440-021-00410-9