Nonexistence of periodic solutions of a complex Riccati equation (Q1907727)

The authors prove that there exists a function \(p : \mathbb{R} \to \mathbb{C}\) smooth and \(2 \pi\)-periodic such that \(z' = z^2 + p(t)\) has no \(2 \pi\)-periodic solutions. The problem of existence or nonexistence of periodic solutions for these equations has been recently posed by \textit{J. Mawhin} [Differ. Integral Equ. 7, No. 3-4, 1055-1061 (1994; Zbl 0802.34045)].