NONLINEAR NEUMANN EQUATIONS DRIVEN BY A NONHOMOGENEOUS DIFFERENTIAL OPERATOR

被引：21

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

共 40 条

[1] THE SPECTRUM AND AN INDEX FORMULA FOR THE NEUMANN p-LAPLACIAN AND MULTIPLE SOLUTIONS FOR PROBLEMS WITH A CROSSING NONLINEARITY [J].

Aizicovici, S. ;

Papageorgiou, N. S. ;

Staicu, V. .

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2009, 25 (02) :431-456

[2]

Aizicovici S., 2008, MEMOIRS AMS, V196

[3] Existence of multiple solutions with precise sign information for superlinear Neumann problems [J].

Aizicovici, Sergiu ;

Papageorgiou, Nikolaos S. ;

Staicu, Vasile .

ANNALI DI MATEMATICA PURA ED APPLICATA, 2009, 188 (04) :679-715

[4] SOLVABILITY FOR SOME BOUNDARY VALUE PROBLEMS WITH φ-LAPLACIAN OPERATORS [J].

Angel Cid, J. ;

Torres, Pedro J. .

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2009, 23 (03) :727-732

[5]

[Anonymous], 1968, LINEAR QUASILINEAR E

[6]

[Anonymous], 2003, FIXED POINT THEOR-RO, DOI DOI 10.1007/978-0-387-21593-8

[7] Sobolev versus Holder local minimizers and global multiplicity for some quasilinear elliptic equations [J].

Azorero, JPG ;

Alonso, IP ;

Manfredi, JJ .

COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, 2000, 2 (03) :385-404

[8] ABSTRACT CRITICAL-POINT THEOREMS AND APPLICATIONS TO SOME NON-LINEAR PROBLEMS WITH STRONG RESONANCE AT INFINITY [J].

BARTOLO, P ;

BENCI, V ;

FORTUNATO, D .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1983, 7 (09) :981-1012

[9] Critical point theory for asymptotically quadratic functionals and applications to problems with resonance [J].

Bartsch, T ;

Li, SJ .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1997, 28 (03) :419-441

[10]

BREZIS H, 1993, CR ACAD SCI I-MATH, V317, P465

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