NONLINEAR NEUMANN EQUATIONS DRIVEN BY A NONHOMOGENEOUS DIFFERENTIAL OPERATOR

被引：20

作者：

Hu, Shouchuan ^{[1
,2
]}

Papageorgiou, Nikolaos S. ^{[3
]}

机构：

[1] Shandong Normal Univ, Coll Math, Jinan, Shandong, Peoples R China

[2] Missouri State Univ, Dept Math, Springfield, MO 65804 USA

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

来源：

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS | 2011年 / 10卷 / 04期

关键词：

C-condition; nonlinear regularity; critical group; Morse relation; Mountain Pass theorem; Moser iteration method; P-LAPLACIAN; MULTIPLE SOLUTIONS; LOCAL MINIMIZERS; EXISTENCE; RESONANCE; THEOREMS; FORMULA;

D O I：

10.3934/cpaa.2011.10.1055

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider a nonlinear Neumann problem driven by a nonhomogeneous nonlinear differential operator and with a reaction which is (p - 1)-superlinear without necessarily satisfying the Ambrosetti-Rabinowitz condition. A particular case of our differential operator is the p-Laplacian. By combining variational methods based on critical point theory with truncation techniques and Morse theory, we show that the problem has at least three nontrivial smooth solutions, two of which have constant sign (one positive and the other negative).

引用

页码：1055 / 1078

页数：24

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