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

被引：0

作者：

Papageorgiou, Nikolaos S. ^{[1
]}

Radulescu, Vicentiu D. ^{[2
,3
,4
,5
,6
]}

Sun, Xueying ^{[4
,7
]}

机构：

[1] Natl Tech Univ Athens, Dept Math, Zografou Campus, Athens 15780, Greece

[2] AGH Univ Krakow, Fac Appl Math, al Mickiewicza 30, PL-30059 Krakow, Poland

[3] Brno Univ Technol, Fac Elect Engn & Commun, Technicka 3058-10, Brno 61600, Czech Republic

[4] Univ Craiova, Dept Math, Craiova 200585, Romania

[5] Zhejiang Normal Univ, Sch Math, Jinhua 321004, Zhejiang, Peoples R China

[6] Romanian Acad, Simion Stoilow Inst Math, Bucharest 010702, Romania

[7] Harbin Engn Univ, Coll Math Sci, Harbin 150001, Peoples R China

来源：

MILAN JOURNAL OF MATHEMATICS | 2023年 / 91卷 / 02期

关键词：

Nonautonomous differential operator; Eigenvalue problem; Indefinite potential; Noncoercive perturbation; Picone's identity; Regularity and comparison results; POSITIVE SOLUTIONS; EXISTENCE;

D O I：

10.1007/s00032-023-00385-2

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

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.

引用

页码：353 / 373

页数：21

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