Eliseenko, M. N. On periodic solutions of second order ordinary differential equations not in explicit form with respect to the derivative. (Russian) Zbl 0604.34023 Differ. Uravn. 21, No. 9, 1618-1621 (1985). Consider the system of differential equations in vector form (1) \(\ddot x=A(t)x+f(t,x,\dot x,\ddot x),\) \(x\in R^ n\), A(t) is a continuous \(n\times n\) matrix \(\omega\)-periodic in t, f is continuous in its arguments, \(\omega\)-periodic in t, and satisfies Lipschitz conditions. The author proves that under certain conditions the system (1) has a unique \(\omega\)-periodic solution and presents a scheme for its construction. Reviewer: G.Bojadziev Cited in 1 Document MSC: 34C25 Periodic solutions to ordinary differential equations Keywords:second order differential equation; Lipschitz conditions PDFBibTeX XMLCite \textit{M. N. Eliseenko}, Differ. Uravn. 21, No. 9, 1618--1621 (1985; Zbl 0604.34023)