Author:
Alwash M. A. M.,Lloyd N. G.
Abstract
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.
Publisher
Cambridge University Press (CUP)
Reference12 articles.
1. The Number of Periodic Solutions of the Equation Ż=z
N
+p
1
(t
)z
N
−1
+…+p
N
(t
)
2. Some problems in the qualitative theory of ordinary differential equations;Yanqian;J. Differential Equations,1982
3. Small amplitude limit cycles of polynomial differential equations
4. 1 Alwash M. A. M. and Lloyd N. G. . Periodic solutions of a quartic non-autonomous equation. Nonlinear Anal, (to appear).
5. On the number of limit cycles which appear with the variation of coefficients from anequilibrium position of focus or centre type;Bautin;Mat. Sb.,1952
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