LIMIT CYCLES FOR SOME ABEL EQUATIONS HAVING COEFFICIENTS WITHOUT FIXED SIGNS

被引：28

作者：

Bravo, J. L. ^{[1
]}

Fernandez, M. ^{[1
]}

Gasull, A. ^{[2
]}

机构：

[1] Univ Extremadura, Dept Matemat, E-06071 Badajoz, Spain

[2] Univ Autonoma Barcelona, Dept Matemat, E-08193 Barcelona, Spain

来源：

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS | 2009年 / 19卷 / 11期

关键词：

Abel equation; periodic solution; limit cycle; TWO-DIMENSIONAL SYSTEMS; DIFFERENTIAL-EQUATIONS; PERIODIC-SOLUTIONS; CUBIC SYSTEMS; NUMBER; UNIQUENESS;

D O I：

10.1142/S0218127409025195

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that some 2 pi-periodic generalized Abel equations of the form x' = A(t)x(n) + B(t)x(m) + C(t)x, with n not equal m and n, m >= 2 have at most three limit cycles. The novelty of our result is that, in contrast with other results of the literature, our hypotheses allow the functions A, B, and C to change sign. Finally we study in more detail the Abel equation x' = A(t)x(3) + B(t)x(2), where the functions A and B are trigonometric polynomials of degree one.

引用

页码：3869 / 3876

页数：8

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