THREE NONTRIVIAL SOLUTIONS FOR PERIODIC PROBLEMS WITH THE p-LAPLACIAN AND A p-SUPERLINEAR NONLINEARITY

被引：7

作者：

Gasinski, Leszek ^{[1
]}

Papageorgiou, Nikolaos S. ^{[2
]}

机构：

[1] Jagiellonian Univ, Inst Comp Sci, PL-30072 Krakow, Poland

[2] Natl Tech Univ Athens, Dept Math, Athens 15780, Greece

来源：

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS | 2009年 / 8卷 / 04期

关键词：

Scalar p-Laplacian; mountain pass theorem; critical groups; Morse theory; Poincare-Hopf formula; ELLIPTIC PROBLEMS; EQUATIONS; EXISTENCE; RESONANCE; INFINITY; DRIVEN;

D O I：

10.3934/cpaa.2009.8.1421

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider a nonlinear periodic problem driven by the scalar p-Laplacian and a nonlinearity that exhibits a p-superlinear growth near +/-infinity, but need not satisfy the Ambrosetti-Rabinowitz condition. Using minimax methods, truncations techniques and Morse theory, we show that the problem has at least three nontrivial solutions, two of which are of fixed sign.

引用

页码：1421 / 1437

页数：17

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