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On some boundary value problems for the Lipschitz differential equations. (Russian) Zbl 0946.34016

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.

MSC:

34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations
34C25 Periodic solutions to ordinary differential equations

Citations:

Zbl 0930.65084
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