A Note on the Asymptotic Stability of Periodic Solutions of Autonomous Differential Equations

SIAM Review ◽  
1984 ◽  
Vol 26 (3) ◽  
pp. 417-421 ◽  
Author(s):  
H. Arthur De Kleine
Keyword(s):  
Asymptotic Stability ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Autonomous Differential Equations

Non-autonomous equations related to polynomial two-dimensional systems

1987 ◽  
Vol 105 (1) ◽  
pp. 129-152 ◽  
Author(s):  
M. A. M. Alwash ◽  
N. G. Lloyd
Keyword(s):  
Differential Equations ◽  
Periodic Solutions ◽  
Sufficient Conditions ◽  
Two Dimensional ◽  
One Dimensional ◽  
Introductory Section ◽  
Independent Variable ◽  
Autonomous Differential Equations

SynopsisPeriodic solutions of certain one-dimensional non-autonomous differential equations are investigated (equation (1.4)); the independent variable is complex. The motivation, which is explained in the introductory section, is the connection with certain polynomial two-dimensional systems. Several classes of coefficients are considered; in each case the aim is to estimate the maximum number of periodic solutions into which a given solution can bifurcate under perturbation of the coefficients. In particular, we need to know when there is a full neighbourhood of periodic solutions. We give a number of sufficient conditions and investigate the implications for the corresponding two-dimensional systems.

Periodic solutions of polynomial non-autonomous differential equations

1993 ◽  
Vol 123 (5) ◽  
pp. 783-801 ◽  
Author(s):  
J. Devlin
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Periodic Functions ◽  
Autonomous Differential Equations ◽  
Image Position ◽  
The Way

Let ℐN denote the set of (N + 1)-tuples of C1 ω-periodic functions; the point P = (pN,…, p1p0) ϵ ℐN is identified with the differential equationWe examine the way in which the total number of ω-periodic solutions can vary as P traverses a path in ℐN.

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