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Research Article | Open Access

Anisotropic (p→,q→)-Laplacian problems with superlinear nonlinearities

Eleonora Amoroso1, Angela Sciammetta2, Patrick Winkert3( )
Department of Engineering, University of Messina, 98166 Messina, Italy
Department of Mathematics and Computer Science, University of Palermo, 90123 Palermo, Italy
Technische Universität Berlin, Institut für Mathematik, Straße des 17. Juni 136, 10623 Berlin, Germany
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Abstract

In this paper we consider a class of anisotropic (p→,q→)-Laplacian problems with nonlinear right-hand sides that are superlinear at ±∞. 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.

Keywords

anisotropic problemscritical point theoryexistencemultiplicity resultslocation of the solutionsparametric problemsuperlinear nonlinearity
CLC number: 35A01, 35D30, 35J62, 35J66

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Communications in Analysis and Mechanics
Volume 16 Issue 1,
February 2024
Pages 1-23
DOI: 10.3934/cam.2024001

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Cite this article:
Amoroso E, Sciammetta A, Winkert P. Anisotropic (p→,q→)-Laplacian problems with superlinear nonlinearities. Communications in Analysis and Mechanics, 2024, 16(1): 1-23. https://doi.org/10.3934/cam.2024001

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Received: 22 September 2023
Revised: 15 December 2023
Accepted: 02 January 2024
Published: 08 January 2024
©2024 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)