On Periodic Solutions of Planar Polynomial Differential Equations with Periodic Coefficients

✍ Scribed by R. Srzednicki

• Publisher: Elsevier Science
• Year: 1994
• Tongue: English
• Weight: 743 KB
• Volume: 114
• Category: Article
• ISSN: 0022-0396
• DOI: 10.1006/jdeq.1994.1141

✦ Synopsis

We consider the planar equation (\dot{z}=\sum a_{k, l}(t) z^{k} \bar{z}^{l}), where (a_{k, l}) is a (T)-periodic complex-valued continuous function, equal to 0 for almost all (k, l \in \mathbb{N}). We present sufficient conditions imposed on (a_{k,}), which guarantee the existence of its (T)-periodic solutions and, in the case (a_{0,0}=0), the conditions for the existence of nonzero ones. We use a method which computes the fixed point index of the Poincare-Andronov operator in isolated sets of fixed points generated by so-called periodic blocks. The method is based on the Lefschetz fixed point theorem and the topological principle of Ważewski. 1994 Academic Press, Inc.