Ronto, A. N. On some boundary value problems for the Lipschitz differential equations. (Russian) Zbl 0946.34016 Nelinijni Kolyvannya 1998, No. 1, 74-94 (1998). The paper addresses the periodic boundary value problem \[ \frac{dx}{dt}=f(t,x(t)),\quad t\in[0,\omega],\quad x(0)=x(\omega),\tag{1} \] with \(x:[0,\omega]\to{\mathbb{R}}^n\), \(f:[0,\omega]\times \Omega\to {\mathbb{R}}^n\), \( \Omega\subset{\mathbb{R}}^n\), \( f(t,x)\) satisfies the Carathéodory conditions. The numerical analytical method for constructing periodic solutions by A. M. Samoilenko and N. I. Ronto [Numerical-analytic methods in the theory of boundary value problems for ordinary differential equations, Kiev: Naukova Dumka (1992; Zbl 0930.65084)]is extended to system (1). The application of the proposed generalization to concrete systems is not discussed. Reviewer: A. A. Martynyuk (Kyïv) Cited in 1 Document MSC: 34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations 34C25 Periodic solutions to ordinary differential equations Keywords:periodic boundary value problem; existence of solutions; Lipschitz differential equations Citations:Zbl 0930.65084 PDFBibTeX XMLCite \textit{A. N. Ronto}, Neliniĭni Kolyvannya 1998, No. 1, 74--94 (1998; Zbl 0946.34016)