Multiple periodic solutions of scalar second order differential equations

被引：15

作者：

Fonda, Alessandro ^{[1
]}

Ghirardelli, Luca ^{[2
]}

机构：

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

[2] Scuola Int Super Studi Avanzati, SISSA, I-34151 Trieste, Italy

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2010年 / 72卷 / 11期

关键词：

Multiplicity of periodic solutions; Nonlinear boundary value problems; Poincare-Birkhoff Theorem;

D O I：

10.1016/j.na.2010.01.032

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove multiplicity of periodic solutions for a scalar second order differential equation with an asymmetric nonlinearity, thus generalizing previous results by Lazer and McKenna (1987)[1] and Del Pino, Manasevich and Murua (1992) [2]. The main improvement lies in the fact that we do not require any differentiability condition on the nonlinearity. The proof is based on the use of the Poincare-Birkhoff Fixed Point Theorem. (C) 2010 Elsevier Ltd. All rights reserved.

引用

页码：4005 / 4015

页数：11

共 8 条

[1] Half-eigenvalues of periodic Sturm-Liouville problems [J].

Binding, PA ;

Rynne, BP .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2004, 206 (02) :280-305

[2] ON THE NUMBER OF 2-PI PERIODIC-SOLUTIONS FOR U'' + G(U) = S(1+H(T)) USING THE POINCARE-BIRKHOFF THEOREM [J].

DELPINO, MA ;

MANASEVICH, RF ;

MURUA, A .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1992, 95 (02) :240-258

[3] A GENERALIZATION OF THE POINCARE-BIRKHOFF THEOREM [J].

DING, WY .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1983, 88 (02) :341-346

[4] NONLINEAR INTEGRAL EQUATIONS OF THE HAMMERSTEIN TYPE [J].

DOLPH, CL .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1949, 66 (JUL-) :289-307

[5]

LAZER AC, 1987, ANN I H POINCARE-AN, V4, P243

[6] Multiplicity results for periodic solutions of second order ODEs with asymmetric nonlinearities [J].

Rebelo, C ;

Zanolin, F .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1996, 348 (06) :2349-2389

[7]

Rebelo C., 1997, DISCRETE CONTIN DYN, V3, P25, DOI DOI 10.3934/DCDS.1997.3.25

[8]

Zanini C, 2005, DYNAM CONT DIS SER A, V12, P343

← 1 →