On periodic solutions of planar polynomial differential equations with periodic coefficients (Q1338297)

A differential equation (1) \(\dot z = \sum_{p + q = m} a_{pq} e^{i \varphi (q+1-p)t} z^ p \overline z^ q + b(t,z)\) is studied where \(m \geq 2\), \(\varphi\), \(T \in R\), \(T>0\), \(k \in N\), \(b:R^ 2 \to R^ 2\) is continuous and \(T\)-periodic in \(t\), \(b(t,z)/ | z |^ m \to 0\) if \(| z | \to \infty\) uniformly in \(t\). Further, \(a_{pq} = 0\) unless \(p - q = 1 \text{mod} k\). Sufficient conditions are given under which (1) has a \(T\)-periodic solution.