Periodic solutions of some planar non-autonomous polynomial differential
The main result of the paper is a theorem on existence of \(T\)-periodic solutions of the planar equation \(\bar z'= \sum_{0\leq k+l< r+s} b_{kl}(t)\bar z^ k z^ l+ c\bar z^ r z^ s\) under the assumption that \(b_{kl}\) are \(T\)-periodic, \(r+s\geq 1\) and that either \(r\leq s- 1\) and \(c\neq 0\) or \(r= s+1\) and the real part of \(c\) is nonzero. This extends a previous result on the equation in which \(c\) was assumed to be real. The proof in the paper is based on a version of the Mawhin Theorem on solutions of nonlinear coincidence equations. Some remarks concerning related ordinary differential equations or systems are also included.
nonautonomous polynomial differential equations
scientific article; zbMATH DE number 597504