Title

On Variational Inequalities with Multivalued Perturbing Terms Depending on Gradients

Author

Vy Khoi Le

Abstract

In this paper, we study variational inequalities of the form {⟨A(u),v-u⟩+⟨F(u),v-u⟩+J(v)-J(u)≥0,∀v∈Xu∈X,where A and F are multivalued operators represented by integrals, J is a convex functional, and X is a Sobolev space of variable exponent. The principal term A is a multivalued operator of Leray-Lions type. We concentrate on the case where F is given by a multivalued function f= f(x, u, ∇ u) that depends also on the gradient ∇ u of the unknown function. Existence of solutions in coercive and noncoercive cases are considered. In the noncoercive case, we follow a sub-supersolution approach and prove the existence of solutions of the above inequality under a multivalued Bernstein-Nagumo type condition.

Department(s)

Mathematics and Statistics

Comments

Article in press

Keywords and Phrases

Bernstein-Nagumo condition; Generalized pseudomonotone mapping; Multivalued mapping; Sobolev space with variable exponent; Variational inequality

International Standard Serial Number (ISSN)

0971-3514; 0974-6870

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2017 Foundation for Scientific Research and Technological Innovation, All rights reserved.

Publication Date

16 Jan 2017

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