Indefinite perturbations of an unbalanced growth eigenvalue problem

We consider indefinite perturbations of a double-phase eigenvalue problem. The perturbation is sublinear or superlinear, and it is in general sign-changing. Using the Nehari manifold, we prove the existence of two constant sign solutions for both cases (sublinear and superlinear), when the parameter \lambda\in (0,\hat{\lambda}^{\alpha}_{1}) with \hat{\lambda}^{\alpha}_{1}>0 being the principal eigenvalue of Dirichlet weighted p -Laplace operator -\Delta^{\alpha}_{p} .

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Publication Details

Journal
Zeitschrift für Analysis und ihre Anwendungen
Published
2024-11-08
DOI
https://doi.org/10.4171/zaa/1782
Primary Topic
Nonlinear Differential Equations Analysis
Type
article
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article

Indefinite perturbations of an unbalanced growth eigenvalue problem

Yunru Bai, Shengda Zeng, Nikolaos S. Papageorgiou
Zeitschrift für Analysis und ihre Anwendungen
Nonlinear Differential Equations Analysis
article

Indefinite perturbations of an unbalanced growth eigenvalue problem

Yunru Bai, Shengda Zeng, Nikolaos S. Papageorgiou
article en

Abstract

We consider indefinite perturbations of a double-phase eigenvalue problem. The perturbation is sublinear or superlinear, and it is in general sign-changing. Using the Nehari manifold, we prove the existence of two constant sign solutions for both cases (sublinear and superlinear), when the parameter \lambda\in (0,\hat{\lambda}^{\alpha}_{1}) with \hat{\lambda}^{\alpha}_{1}>0 being the principal eigenvalue of Dirichlet weighted p -Laplace operator -\Delta^{\alpha}_{p} .

Zeitschrift für Analysis und ihre AnwendungenVol. 45(1)
Chongqing Normal University (CN), Guangxi University (CN), National Technical University of Athens (GR), Guangxi University of Science and Technology (CN), Guangxi Science and Technology Department (CN)
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Nonlinear Differential Equations Analysis
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