Anisotropic (p, q) Equation with Partially Concave Terms

We consider a Dirichlet problem driven by the anisotropic (p,q) Laplacian. In the reaction, we have a parametric partially concave term plus a “superlinear” perturbation (convex term) which need not satisfy the Ambrosetti–Rabinowitz condition. Using variational tools, we show that for all small values of the parameter λ>0, the problem has at least two nontrivial smooth solutions.

Authors

Nikolaos S. Papageorgiou (ORCID: https://orcid.org/0000-0003-4800-1187)
Leszek Gasiński (ORCID: https://orcid.org/0000-0001-8692-6442)
Gregoris Makrides

Institutions

National Technical University of Athens (GR)
University School of Physical Education in Kraków (PL)
University of Craiova (RO)

Publication Details

Journal: Symmetry
Published: 2024-09-10
DOI: https://doi.org/10.3390/sym16091188
Primary Topic: Nonlinear Partial Differential Equations
Type: article
Field-Weighted Citation Impact: 0.00

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article

Anisotropic (p, q) Equation with Partially Concave Terms

Nikolaos S. Papageorgiou, Leszek Gasiński, Gregoris Makrides

Sep 10, 2024

Symmetry

Nonlinear Partial Differential Equations

article

Anisotropic (p, q) Equation with Partially Concave Terms

Nikolaos S. Papageorgiou, Leszek Gasiński, Gregoris Makrides

September 10, 2024article en

Abstract

We consider a Dirichlet problem driven by the anisotropic (p,q) Laplacian. In the reaction, we have a parametric partially concave term plus a “superlinear” perturbation (convex term) which need not satisfy the Ambrosetti–Rabinowitz condition. Using variational tools, we show that for all small values of the parameter λ>0, the problem has at least two nontrivial smooth solutions.

SymmetryVol. 16(9)

National Technical University of Athens (GR), University School of Physical Education in Kraków (PL), University of Craiova (RO)

Openalex Percentile: Top 74%

Nonlinear Partial Differential Equations

DOI Open Access PDF OpenAlex

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