Anisotropic Robin problems with indefinite potential

Nikolaos S. Papageorgiou; Vicenţiu D. Rădulescu; Jian Zhang; Nikolaos S. Papageorgiou; Vicenţiu D. Rădulescu; Jian Zhang

doi:10.3934/era.2025302

Electronic Research Archive

2025, Volume 33, Issue 11: 6844-6864. doi: 10.3934/era.2025302

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Anisotropic Robin problems with indefinite potential

1.
Department of Mathematics, National Technical University, Zografou Campus, Athens 15780, Greece
2.
Center for Applied Mathematics, Yulin Normal University, Yulin 537000, China
3.
Department of Mathematics, University of Craiova, 200585 Craiova, Romania
4.
Faculty of Applied Mathematics, AGH University of Kraków, 30-059 Kraków, Poland
5.
Faculty of Electrical Engineering and Communication, Brno University of Technology, Technická 3058/10, Brno 61600, Czech Republic
6.
"Simion Stoilow" Institute of Mathematics of the Romanian Academy, P.O. Box 1-764, 014700 Bucharest, Romania
7.
School of Mathematics and Statistics, Hunan University of Technology and Business, Changsha 410205, China
This paper is dedicated with esteem to Professor Patrizia Pucci on the occasion of her anniversary.

Received: 23 September 2025 Revised: 03 November 2025 Accepted: 07 November 2025 Published: 17 November 2025

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.
- variable exponents,
- regularity theory,
- constant sign and nodal solutions,
- critical point theory,
- critical groups
Citation: Nikolaos S. Papageorgiou, Vicenţiu D. Rădulescu, Jian Zhang. Anisotropic Robin problems with indefinite potential[J]. Electronic Research Archive, 2025, 33(11): 6844-6864. doi: 10.3934/era.2025302

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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.

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