Nonlinear evolutionary systems driven by mixed variational inequalities and its applications
By Zhenhai Liu, Dumitru Motreanu, Shengda Zeng. Nonlinear Analysis: Real world applications, 2018
62 citations recorded by the source corpus.
Abstract In this paper we investigate the system obtained by mixing a nonlinear evolutionary equation and a mixed variational inequality ((EEVI), for short) on Banach spaces in the case where the set of constraints is not necessarily compact and the problem is driven by a ϕ -pseudomonotone operator which is not necessarily monotone. In this way, we extend the recent results in Liu–Zeng–Motranu, (2016). First, it is shown that the solution set for the mixed variational inequality associated to problem (EEVI) is nonempty, closed, convex and bounded. Upper semicontinuity and measurability properties are also established. Then, relying on these results, we prove the existence of solutions for problem (EEVI) as well as a compactness property for the solution set. Finally, as an application, we study a new class of partial differential complementarity problems.
Subfields: Civil and Structural Engineering, Computational Theory and Mathematics
View Paper: https://www.semanticscholar.org/paper/1cee2d6eb9fc201a955fe93176849bf5556bfe14
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Citations in the corpus
- A class of fractional differential hemivariational inequalities with application to contact problem (2018, background): “[31] have provided existence results for a class of differential mixed variational inequalities in Banach spaces exploiting the semigroup theory, theory of measure of noncompactness, the Filippov implicit function lemma, and a fixed point theorem for condensing set-valued operators, etc.”