Abstract
In this article, we examine variational inequalities of the form (Formula presented.), where (Formula presented.) is a generalized fractional (Formula presented.) -Laplace operator, K is a closed convex set in a fractional Musielak–Orlicz–Sobolev space, and (Formula presented.) is a multivalued integral operator. We consider a functional analytic framework for the above problem, including conditions on the multivalued lower order term (Formula presented.) such that the problem can be properly formulated in a fractional Musielak–Orlicz–Sobolev space, and the involved mappings have certain useful monotonicity–continuity properties. Furthermore, we investigate the existence of solutions contingent upon certain coercivity conditions.
Recommended Citation
V. K. Le, "Multivalued Variational Inequalities with Generalized Fractional Φ-Laplacians," Fractal and Fractional, vol. 8, no. 6, article no. 324, MDPI, Jun 2024.
The definitive version is available at https://doi.org/10.3390/fractalfract8060324
Department(s)
Mathematics and Statistics
Publication Status
Open Access
Keywords and Phrases
fractional Laplacian; fractional Musielak–Orlicz space; fractional Musielak–Orlicz–Sobolev space; multivalued mapping; pseudomonotone mapping; variational inequality
International Standard Serial Number (ISSN)
2504-3110
Document Type
Article - Journal
Document Version
Final Version
File Type
text
Language(s)
English
Rights
© 2024 The Authors, All rights reserved.
Creative Commons Licensing
This work is licensed under a Creative Commons Attribution 4.0 License.
Publication Date
01 Jun 2024
