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Nonlinear evolutionary systems driven by quasi‐hemivariational inequalities
Author(s) -
Liu Zhenhai,
Motreanu Dumitru,
Zeng Shengda
Publication year - 2018
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4660
Subject(s) - mathematics , nonlinear system , banach space , solution set , monotonic function , compact space , set (abstract data type) , subderivative , regular polygon , inequality , mixing (physics) , mathematical analysis , convex optimization , geometry , computer science , physics , quantum mechanics , programming language
This paper is devoted to the study of the differential systems in arbitrary Banach spaces that are obtained by mixing nonlinear evolutionary equations and generalized quasi‐hemivariational inequalities (EEQHVI). We start by showing that the solution set of the quasi‐hemivariational inequality associated to problem EEQHVI is nonempty, closed, and convex. Furthermore, we establish upper semicontinuity and measurability properties for this solution set. Then, based on them, we prove the existence of solutions for problem EEQHVI and the compactness of the set of corresponding trajectories of EEQHVI. These statements extend previous results in several directions, for instance, by dropping the boundedness requirement for the set of constraints and substantially relaxing monotonicity hypotheses.