Multiplicity of periodic solutions for the planar polynomial equation

被引：8

作者：

Borisovich, A ^{[1
]}

Marzantowicz, W

机构：

[1] Univ Gdansk, Inst Math, PL-80952 Gdansk, Poland

[2] Adam Mickiewicz Univ, Fac Math & Informat, Poznan, Poland

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2001年 / 43卷 / 02期

关键词：

planar ODE; periodic coefficients; periodic solutions; averaging; a priori estimate;

D O I：

10.1016/S0362-546X(99)00191-1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A nonautonomous system of ordinary differential equations was studied. The multiplicity problems based on theorems on the multiplicity of distinct roots of a complex polynomial was studied by using Nielson theory. The main theorem gives a sufficient condition for the existence of periodic solutions for a particular equation by direct integration.

引用

页码：217 / 231

页数：15

共 50 条

[31] ON THE PERIODIC SOLUTIONS OF A PARTICULAR LAME EQUATION
Amar, Makhlouf
CELESTIAL MECHANICS & DYNAMICAL ASTRONOMY, 1991, 52 (04) : 397 - 406
[32] Parabolic solutions for the planar N-centre problem: multiplicity and scattering
Boscaggin, Alberto
Dambrosio, Walter
Papini, Duccio
ANNALI DI MATEMATICA PURA ED APPLICATA, 2018, 197 (03) : 869 - 882
[33] A simple proof of multiplicity for periodic solutions of Lagrangian difference systems with relativistic operator and periodic potential
Mawhin, J.
JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS, 2016, 22 (02) : 306 - 315
[34] Existence and Multiplicity of Periodic Solutions to Fractional p-Laplacian Equations
Li, Lin
Tersian, Stepan
DIFFERENTIAL AND DIFFERENCE EQUATIONS WITH APPLICATIONS, 2018, 230 : 495 - 507
[35] MULTIPLICITY OF SOLUTIONS OF VARIATIONAL SYSTEMS INVOLVING φ-LAPLACIANS WITH SINGULAR φ AND PERIODIC NONLINEARITIES
Mawhin, Jean
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2012, 32 (11) : 4015 - 4026
[36] Existence and multiplicity of periodic solutions for some second order Hamiltonian systems
Ye, Yiwei
Tang, Chun-Lei
BULLETIN OF THE BELGIAN MATHEMATICAL SOCIETY-SIMON STEVIN, 2014, 21 (04) : 613 - 633
[37] Periodic solutions for planar four-body problems
Deng, Chunhua
Zhang, Shiqing
JOURNAL OF GEOMETRY AND PHYSICS, 2009, 59 (09) : 1210 - 1215
[38] Existence and multiplicity of periodic solutions for the ordinary p-Laplacian systems
Liao K.
Tang C.-L.
Journal of Applied Mathematics and Computing, 2011, 35 (1-2) : 395 - 406
[39] Multiplicity results for periodic solutions of second order ODEs with asymmetric nonlinearities
Rebelo, C
Zanolin, F
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1996, 348 (06) : 2349 - 2389
[40] Periodic solutions for a nonautonomous ordinary differential equation
Albuquerque Araujo, Anderson Luis
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2012, 75 (05) : 2897 - 2903

← 1 2 3 4 5 →