Existence of solutions for implicit obstacle problems involving nonhomogeneous partial differential operators and multivalued terms
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Date
2021-05-06
Authors
Zeng, Shengda
Bai, Yunru
Gasinski, Leszek
Krech, Ireneusz
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
In this article, we study an implicit obstacle problem with a nonlinear nonhomogeneous partial differential operator and a multivalued operator which is described by a generalized gradient. Under quite general assumptions on the data, and employing Kluge's fixed point principle for multivalued operators, Minty technique and a surjectivity theorem, we prove that the set of weak solutions to the problem is nonempty, bounded and weakly closed.
Description
Keywords
Implicit obstacle problem, Clarke generalized gradient, Nonhomogeneous partial differential operator, Fixed point theorem, Surjectivity theorem
Citation
Zeng, S., Bai, Y., Gasinski, L., & Krech, I. (2021). Existence of solutions for implicit obstacle problems involving nonhomogeneous partial differential operators and multivalued terms. <i>Electronic Journal of Differential Equations, 2021</i>(37), pp. 1-18.
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Attribution 4.0 International