On the qualitative behavior of periodic solutions of differential systems
The method of reflecting functions introduced by V. I. Mironenko is applied to study the existence and stability of \(\omega\)-periodic solutions of the differential system \[ x'=X(t,x) \] with \(X(t,x)\) being \(2\omega\)-periodic in \(t\). Recall that the function \(F(t,x)\) is said a reflective function for the considered system, if \(F\) satisfies the partial differential equation \[ F_t + F_x X(t,x)+X(-t,F)=0\,. \]
scientific article; zbMATH DE number 5608852