Anisotropic $ (\vec{p}, \vec{q}) $-Laplacian problems with superlinear nonlinearities

Eleonora Amoroso; Angela Sciammetta; Patrick Winkert; Eleonora Amoroso; Angela Sciammetta; Patrick Winkert

doi:10.3934/cam.2024001

Communications in Analysis and Mechanics

2024, Volume 16, Issue 1: 1-23. doi: 10.3934/cam.2024001

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Research article

Anisotropic $ (\vec{p}, \vec{q}) $-Laplacian problems with superlinear nonlinearities

1.
Department of Engineering, University of Messina, 98166 Messina, Italy
2.
Department of Mathematics and Computer Science, University of Palermo, 90123 Palermo, Italy
3.
Technische Universität Berlin, Institut für Mathematik, Straße des 17. Juni 136, 10623 Berlin, Germany

Received: 22 September 2023 Revised: 15 December 2023 Accepted: 02 January 2024 Published: 08 January 2024
35A01, 35D30, 35J62, 35J66

In this paper we consider a class of anisotropic $ (\vec{p}, \vec{q}) $-Laplacian problems with nonlinear right-hand sides that are superlinear at $ \pm\infty $. We prove the existence of two nontrivial weak solutions to this kind of problem by applying an abstract critical point theorem under very general assumptions on the data without supposing the Ambrosetti-Rabinowitz condition.
- anisotropic problems,
- critical point theory,
- existence,
- multiplicity results,
- location of the solutions,
- parametric problem,
- $ (\vec{p}, \vec{q}) $-Laplacian,
- superlinear nonlinearity
Citation: Eleonora Amoroso, Angela Sciammetta, Patrick Winkert. Anisotropic $ (\vec{p}, \vec{q}) $-Laplacian problems with superlinear nonlinearities[J]. Communications in Analysis and Mechanics, 2024, 16(1): 1-23. doi: 10.3934/cam.2024001

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Abstract

In this paper we consider a class of anisotropic $ (\vec{p}, \vec{q}) $-Laplacian problems with nonlinear right-hand sides that are superlinear at $ \pm\infty $. We prove the existence of two nontrivial weak solutions to this kind of problem by applying an abstract critical point theorem under very general assumptions on the data without supposing the Ambrosetti-Rabinowitz condition.

References

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