Periodic solutions of Abel differential equations

被引：30

作者：

Alwash, M. A. M. ^{[1
]}

机构：

[1] W Los Angeles Coll, Dept Math, Los Angeles, CA 90230 USA

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2007年 / 329卷 / 02期

关键词：

periodic solution; abel differential equation; rigid system; limit cycle; Hopf bifurcation;

D O I：

10.1016/j.jmaa.2006.07.039

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

For a class of polynomial non-autonomous differential equations of degree n, we use phase plane analysis to show that each equation in this class has n periodic solutions. The result implies that certain rigid two-dimensional systems have at most one limit cycle which appears through multiple Hopf bifurcation. (c) 2006 Elsevier Inc. All rights reserved.

引用

页码：1161 / 1169

页数：9

共 14 条

[1]

Alwash M.A.M., 2005, ELECT J DIFFERENTIAL, V84, P1

[2] NONAUTONOMOUS EQUATIONS RELATED TO POLYNOMIAL TWO-DIMENSIONAL SYSTEMS [J].

ALWASH, MAM ;

LLOYD, NG .

PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 1987, 105 :129-152

[3] PERIODIC-SOLUTIONS OF A QUARTIC NONAUTONOMOUS EQUATION [J].

ALWASH, MAM ;

LLOYD, NG .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1987, 11 (07) :809-820

[4] Periodic solutions of a quartic differential equation and Groebner bases [J].

Alwash, MAM .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 1996, 75 (01) :67-76

[5]

[Anonymous], DIFFER EQU DYN SYST

[6]

CONTI R., 1994, Lecture Notes in Pure and Appl. Math., V152, P21

[7] Limit cycles for rigid cubic systems [J].

Gasull, A ;

Prohens, R ;

Torregrosa, J .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2005, 303 (02) :391-404

[8] Exact number of limit cycles for a family of rigid systems [J].

Gasull, A ;

Torregrosa, J .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2005, 133 (03) :751-758

[9] Hilbert-type numbers for Abel equations, growth and zeros of holomorphic functions [J].

Ilyashenko, Y .

NONLINEARITY, 2000, 13 (04) :1337-1342

[10]

Lins Neto A., 1980, INVENT MATH, V59, P67

← 1 2 →