An exact expression of positive periodic solution for a first-order singular equation

被引：0

作者：

Xin, Yun ^{[1
]}

Cui, Xiaoxiao ^{[2
]}

Liu, Jie ^{[2
]}

机构：

[1] Henan Polytech Univ, Coll Comp Sci & Technol, Jiaozuo 454000, Henan, Peoples R China

[2] Henan Polytech Univ, Sch Math & Informat Sci, Jiaozuo 454000, Henan, Peoples R China

来源：

ADVANCES IN DIFFERENCE EQUATIONS | 2020年 / 2020卷 / 01期

关键词：

First-order singular differential equation; Attractive and repulsive singularities; Indefinite singularity; Positive periodic solution; 34B16; 34B18; 34C25; DIFFERENTIAL-EQUATIONS; SYSTEMS;

D O I：

10.1186/s13662-020-02986-2

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The main purpose of this paper is to obtain an exact expression of the positive periodic solution for a first-order differential equation with attractive and repulsive singularities. Moreover, we prove the existence of at least one positive periodic solution for this equation with an indefinite singularity by applications of topological degree theorem, and give the upper and lower bounds of the positive periodic solution.

引用

页数：9

共 20 条

[1]

Agarwal A., 2003, SINGULAR DIFFERENTIA

[2] Periodic solutions of first order functional differential equations with periodic deviations [J].

Bai, Dingyong ;

Xu, Yuantong .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2007, 53 (09) :1361-1366

[3] Global continua of periodic solutions of singular first-order Hamiltonian systems of N-vortex type [J].

Bartsch, Thomas ;

Gebhard, Bjorn .

MATHEMATISCHE ANNALEN, 2017, 369 (1-2) :627-651

[4] Positive periodic solutions of first-order singular systems [J].

Chen, Ruipeng ;

Ma, Ruyun ;

He, Zhiqian .

APPLIED MATHEMATICS AND COMPUTATION, 2012, 218 (23) :11421-11428

[5] Damped superlinear Duffing equation with strong singularity of repulsive type [J].

Cheng, Zhibo ;

Yuan, Qigang .

JOURNAL OF FIXED POINT THEORY AND APPLICATIONS, 2020, 22 (02)

[6] PERIODIC SOLUTION FOR SECOND ORDER DAMPED DIFFERENTIAL EQUATIONS WITH ATTRACTIVE-REPULSIVE SINGULARITIES [J].

Cheng, Zhibo ;

Ren, Jingli .

ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, 2018, 48 (03) :753-768

[7] Positive Periodic Solutions for a Kind of Second-Order Neutral Differential Equations with Variable Coefficient and Delay [J].

Cheng, Zhibo ;

Li, Feifan .

MEDITERRANEAN JOURNAL OF MATHEMATICS, 2018, 15 (03)

[8] Impulsive periodic solutions of first-order singular differential equations [J].

Chu, Jifeng ;

Nieto, Juan J. .

BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 2008, 40 :143-150

[9] Positive Periodic Solutions for a Kind of First-Order Singular Differential Equation Induced by Impulses [J].

Kong, Fanchao ;

Luo, Zhiguo .

QUALITATIVE THEORY OF DYNAMICAL SYSTEMS, 2018, 17 (02) :375-386

[10] ON PERIODIC-SOLUTIONS OF NONLINEAR DIFFERENTIAL-EQUATIONS WITH SINGULARITIES [J].

LAZER, AC ;

SOLIMINI, S .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1987, 99 (01) :109-114

← 1 2 →