Nonhomogeneous singular equations with an indefinite potential and a superlinear perturbation

We consider a Dirichlet problem driven by the (p,q)-Laplacian long with an indefinite potential term. In the reaction, we have the effects of a parametric singular term plus a superlinear Carathèodory perturbation. No Ambrosetti-Rabinowitz condition or any of its variants is used. Using variational tools together with truncation and comparison techniques, we prove a bifurcation-type result: an existence and multiplicity theorem that is global in the parameter $ \lambda>0 $.

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Publication Details

Journal
Discrete and Continuous Dynamical Systems - S
Published
2025-10-16
DOI
https://doi.org/10.3934/dcdss.2025149
Primary Topic
Advanced Mathematical Physics Problems
Type
article
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article

Nonhomogeneous singular equations with an indefinite potential and a superlinear perturbation

Anass Ourraoui, Nikolaos S. Papageorgiou
Discrete and Continuous Dynamical Systems - S
Advanced Mathematical Physics Problems
article

Nonhomogeneous singular equations with an indefinite potential and a superlinear perturbation

Anass Ourraoui, Nikolaos S. Papageorgiou
article en

Abstract

We consider a Dirichlet problem driven by the (p,q)-Laplacian long with an indefinite potential term. In the reaction, we have the effects of a parametric singular term plus a superlinear Carathèodory perturbation. No Ambrosetti-Rabinowitz condition or any of its variants is used. Using variational tools together with truncation and comparison techniques, we prove a bifurcation-type result: an existence and multiplicity theorem that is global in the parameter $ \lambda>0 $.

Discrete and Continuous Dynamical Systems - SVol. 19(0)
National Technical University of Athens (GR)
Openalex Percentile: Top 64%
Advanced Mathematical Physics Problems
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