Radially symmetric systems with a singularity and asymptotically linear growth

被引：28

作者：

Fonda, Alessandro ^{[1
]}

Toader, Rodica ^{[2
]}

机构：

[1] Univ Trieste, Dipartimento Matemat & Informat, I-34127 Trieste, Italy

[2] Univ Udine, Dipartimento Ingn Civile & Architettura, I-33100 Udine, Italy

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2011年 / 74卷 / 07期

关键词：

Periodic solutions; Systems with singularity; Nonlinear dynamics; 2ND-ORDER DIFFERENTIAL-EQUATIONS; COLLISION PERIODIC-SOLUTIONS; NONLINEAR ELASTICITY; WEAK SINGULARITIES; DYNAMICAL-SYSTEMS; REPULSIVE TYPE; FORCE;

D O I：

10.1016/j.na.2010.12.004

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove the existence of infinitely many periodic solutions for radially symmetric systems with a singularity of repulsive type. The nonlinearity is assumed to have a linear growth at infinity, being controlled by two constants which have a precise interpretation in terms of the Dancer-Fucik spectrum. Our result generalizes an existence theorem by Del Pino et al. (1992) [4], obtained in the case of a scalar second order differential equation. (C) 2010 Elsevier Ltd. All rights reserved.

引用

页码：2485 / 2496

页数：12

共 30 条

[1]

Bonheure D., 2003, TOPOL METHOD NONL AN, V22, P297

[2] A CONTINUATION APPROACH TO SUPERLINEAR PERIODIC BOUNDARY-VALUE-PROBLEMS [J].

CAPIETTO, A ;

MAWHIN, J ;

ZANOLIN, F .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1990, 88 (02) :347-395

[3] Non-collision periodic solutions of second order singular dynamical systems [J].

Chu, Jifeng ;

Franco, Daniel .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2008, 344 (02) :898-905

[4]

COTIZELATI V, 1988, NONLINEAR ANAL, V12, P209

[5] T-PERIODIC SOLUTIONS FOR SOME 2ND-ORDER DIFFERENTIAL-EQUATIONS WITH SINGULARITIES [J].

DELPINO, M ;

MANASEVICH, R ;

MONTERO, A .

PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 1992, 120 :231-243

[6] INFINITELY MANY T-PERIODIC SOLUTIONS FOR A PROBLEM ARISING IN NONLINEAR ELASTICITY [J].

DELPINO, MA ;

MANASEVICH, RF .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1993, 103 (02) :260-277

[7] PERIODIC-SOLUTIONS OF 2ND-ORDER DIFFERENTIAL-EQUATIONS WITH SUPERLINEAR ASYMMETRIC NONLINEARITIES [J].

FABRY, C ;

HABETS, P .

ARCHIV DER MATHEMATIK, 1993, 60 (03) :266-276

[8] PERIODIC-SOLUTIONS FOR A CONSERVATIVE SYSTEM OF DIFFERENTIAL-EQUATIONS WITH A SINGULARITY OF REPULSIVE TYPE [J].

FONDA, A .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1995, 24 (05) :667-676

[9] SUBHARMONIC SOLUTIONS FOR SOME 2ND-ORDER DIFFERENTIAL-EQUATIONS WITH SINGULARITIES [J].

FONDA, A ;

MANASEVICH, R ;

ZANOLIN, F .

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1993, 24 (05) :1294-1311

[10]

FONDA A, ANN MAT PUR IN PRESS

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