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Research Article | Open Access

Anisotropic Robin problems with indefinite potential

Nikolaos S. Papageorgiou1,2,3, Vicenţiu D. Rădulescu3,4,5,6, Jian Zhang7( )
Department of Mathematics, National Technical University, Zografou Campus, Athens 15780, Greece
Center for Applied Mathematics, Yulin Normal University, Yulin 537000, China
Department of Mathematics, University of Craiova, 200585 Craiova, Romania
Faculty of Applied Mathematics, AGH University of Kraków, 30-059 Kraków, Poland
Faculty of Electrical Engineering and Communication, Brno University of Technology, Technická 3058/10, Brno 61600, Czech Republic
"Simion Stoilow" Institute of Mathematics of the Romanian Academy, P.O. Box 1-764, 014700 Bucharest, Romania
School of Mathematics and Statistics, Hunan University of Technology and Business, Changsha 410205, China
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Abstract

We considered a nonlinear elliptic boundary value problem driven by the variable (anisotropic) ( p , q )-Laplacian with Robin boundary condition and a superlinear reaction which does not satisfy the Ambrosetti-Rabinowitz condition. Using critical point theory, truncation and comparison techniques and critical groups, we showed the existence of five nontrivial smooth solutions all with sign information and ordered.

Keywords

variable exponentsregularity theoryconstant sign and nodal solutionscritical point theorycritical groups

References

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Electronic Research Archive
Volume 33 Issue 11,
November 2025
Pages 6844-6864
DOI: 10.3934/era.2025302

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Cite this article:
Papageorgiou NS, Rădulescu VD, Zhang J. Anisotropic Robin problems with indefinite potential. Electronic Research Archive, 2025, 33(11): 6844-6864. https://doi.org/10.3934/era.2025302

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Received: 23 September 2025
Revised: 03 November 2025
Accepted: 07 November 2025
Published: 17 November 2025
©2025 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)