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

[1] The numbers of periodic solutions of the polynomial differential equation
Zhengxin Z.
Journal of Applied Mathematics and Computing, 2004, 16 (1-2) : 265 - 277
[2] Exact Multiplicity and Stability of Periodic Solutions for a Duffing Equation
Liang, S.
MEDITERRANEAN JOURNAL OF MATHEMATICS, 2013, 10 (01) : 189 - 199
[3] Multiplicity of Periodic Solutions for a Higher Order Difference Equation
Hu, Ronghui
ABSTRACT AND APPLIED ANALYSIS, 2014,
[4] Existence and multiplicity of periodic solutions for the Duffing equation with singularity
Xia, Jing
Wang, Zaihong
PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 2007, 137 : 625 - 645
[5] Exact Multiplicity and Stability of Periodic Solutions for a Duffing Equation
S. Liang
Mediterranean Journal of Mathematics, 2013, 10 : 189 - 199
[6] PERIODIC-SOLUTIONS OF A PLANAR DELAY EQUATION
TABOAS, P
PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 1990, 116 : 85 - 101
[7] Multiplicity of positive periodic solutions for delayed difference equation with impulses
Yang X.
Cao J.
Differential Equations and Dynamical Systems, 2009, 17 (3) : 257 - 267
[8] ON PERIODIC-SOLUTIONS OF PLANAR POLYNOMIAL DIFFERENTIAL-EQUATIONS WITH PERIODIC COEFFICIENTS
SRZEDNICKI, R
JOURNAL OF DIFFERENTIAL EQUATIONS, 1994, 114 (01) : 77 - 100
[9] Existence and multiplicity of periodic solutions for a nonlinear resonance equation with singularities
Xiumei Xing
Lingling Wang
Shaoyong Lai
Boundary Value Problems, 2023
[10] Some multiplicity results for periodic solutions of a Rayleigh differential equation
Habets, P
Torres, PJ
DYNAMICS OF CONTINUOUS DISCRETE AND IMPULSIVE SYSTEMS-SERIES A-MATHEMATICAL ANALYSIS, 2001, 8 (03): : 335 - 351

← 1 2 3 4 5 →