Existence results for non-coercive problems

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10.1515_anona20250071.pdf(2.95 MB)
Date
2025-01-01
Authors
Diblík, Josef
Galewski, Marek
Šmarda, Zdeněk
ORCID
0000-0001-5009-316X
 0000-0002-9559-6630
Advisor
Referee
Mark
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Volume Title
Publisher
De Gruyter
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Abstract
In this article, we investigate non-coercive variational equations under assumptions related to generalized monotonicity. We present some general abstract tools regarding the existence of bounded solutions and their multiplicity, which we then apply to the Dirichlet boundary value problem driven by the perturbed (negative) p p -Laplacian. As a by-product of our findings, we provide a version of the Browder-Minty theorem in the potential case that does not involve the Brouwer fixed-point theorem but utilizes optimization techniques.
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Keywords
Dirichlet problem, Minty-Browder theorem, multiple solutions, non-coercive problem, p-Laplacian
Citation
Advances in Nonlinear Analysis. 2025, vol. 14, issue 1, p. 1-13.
https://www.degruyterbrill.com/document/doi/10.1515/anona-2025-0071/html
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Peer-reviewed
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Published version
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Language of document
en
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Creative Commons Attribution 4.0 International
http://creativecommons.org/licenses/by/4.0/
DOI
10.1515/anona-2025-0071
URI
https://hdl.handle.net/11012/255367
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