Electron. J. Differential Equations, Vol. 2021 (2021), No. 37, pp. 1-18.
Existence of solutions for implicit obstacle problems involving nonhomogeneous
partial differential operators and multivalued terms
Shengda Zeng, Yunru Bai, Leszek Gasinski, Ireneusz Krech
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.
Submitted April 1, 2020. Published May 6, 2021.
Math Subject Classifications: 35J20, 35J25, 35J60.
Key Words: Implicit obstacle problem; Clarke generalized gradient;
nonhomogeneous partial differential operator; fixed point theorem;
surjectivity theorem.
DOI: https://doi.org/10.58997/ejde.2021.37
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Shengda Zeng
Guangxi Colleges and Universities Key Laboratory of
Complex System Optimization
and Big Data Processing
Yulin Normal University, Yulin 537000, China
email: zengshengda@163.com
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Yunru Bai
School of Science
Guangxi University of Science and Technology
Liuzhou, Guangxi 545006, China
email: yunrubai@163.com
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Leszek Gasinski
Pedagogical University of Cracow
Department of Mathematics
Podchorazych 2, 30-084 Cracow, Poland
email: leszek.gasinski@up.krakow.pl
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Ireneusz Krech
Pedagogical University of Cracow
Department of Mathematics
Podchorazych 2, 30-084 Cracow, Poland
email: ireneusz.krech@up.krakow.pl
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