On Variational Inequalities with Multivalued Perturbing Terms Depending on Gradients
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.
Recommended Citation
V. K. Le, "On Variational Inequalities with Multivalued Perturbing Terms Depending on Gradients," Differential Equations and Dynamical Systems, vol. 28, pp. 763 - 790, Springer, Oct 2020.
The definitive version is available at https://doi.org/10.1007/s12591-017-0345-y
Department(s)
Mathematics and Statistics
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
01 Oct 2020
Comments
Published online 16 January 2017