On noncoercive elliptic problems

被引：1

作者：

Papageorgiou, Nikolaos S. ^{[1
]}

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

机构：

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

[2] King Abdulaziz Univ, Dept Math, Fac Sci, POB 80203, Jidda 21589, Saudi Arabia

[3] Romanian Acad, Inst Math Simion Stoilow, Bucharest 014700, Romania

来源：

NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS | 2016年 / 23卷 / 04期

关键词：

Positive solution; Nonlinear regularity; Nonlinear maximum principle; Critical groups; Local linking; Nodal solution; SIGN;

D O I：

10.1007/s00030-016-0394-x

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider a nonlinear noncoercive elliptic equation driven by the p-Laplacian. We show that if the L-infinity-perturbation has small norm, then the problem admits a positive solution. Moreover, if the L-infinity-perturbation is nonzero and nonnegative, then we find two positive solutions. Also, we consider a class of semilinear equations with an indefinite and unbounded potential. Using critical groups, we show that there is a nontrivial solution and under a global sign condition, we show that this solutions is nodal. Our results extend and improve a recent work of Radulescu

引用

页数：17

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