Indefinite Perturbations of the Eigenvalue Problem for the Nonautonomous p-Laplacian

被引：0
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作者：
Nikolaos S. Papageorgiou
Vicenţiu D. Rădulescu
Xueying Sun
机构：
[1] National Technical University,Department of Mathematics
[2] Zografou Campus,Faculty of Applied Mathematics
[3] AGH University of Kraków,Faculty of Electrical Engineering and Communication
[4] Brno University of Technology,Department of Mathematics
[5] University of Craiova,School of Mathematics
[6] Zhejiang Normal University,College of Mathematical Sciences
[7] Simion Stoilow Institute of Mathematics of the Romanian Academy,Department of Mathematics
[8] Harbin Engineering University,undefined
[9] University of Craiova,undefined
来源：
Milan Journal of Mathematics | 2023年 / 91卷
关键词：
Nonautonomous differential operator; Eigenvalue problem; Indefinite potential; Noncoercive perturbation; Picone’s identity; Regularity and comparison results; 35B20; 35J20 (Primary); 35J60; 35P30; 47J10; 58E05 (Secondary);
D O I：
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学科分类号：
摘要：
We consider an indefinite perturbation of the eigenvalue problem for the nonautonomous p-Laplacian. The main result establishes an exhaustive analysis in the nontrivial case that corresponds to noncoercive perturbations of the reaction. Using variational tools and truncation and comparison techniques, we prove an existence and multiplicity theorem which is global in the parameter. The main result of this paper establishes the existence of at least two positive solutions in the case of small perturbations, while no solution exists for high perturbations of the quasilinear term in the reaction.
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页码：353 / 373
页数：20
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