Existence of \(2^n\) periodic solutions of a system of \(n\) differential equations of first order
type: Item
instance of: scholarly article
title: Existence of \(2^n\) periodic solutions of a system of \(n\) differential equations of first order
zbMATH Open document ID: 1081.34509
author: M. N. Yakovlev
published in: Journal of Mathematical Sciences (New York)
publication date: 2005-06-24T00:00:00Z
review text: The author considers the problem of the existence of a solution for the system of ordinary differential equations \[ u_i'= f_i(t,u_1,\dots, u_n),\quad 0< t< 1,\quad i= 1,\dots, n, \] with two-point boundary conditions \[ u_i(0)= \Delta_i u_i(1), \] where \(\Delta_i\in \mathbb{R}\), \(f_i(t, u_1,\dots, u_n)\), \(i= 1,\dots, n,\) satisfies the Carathéodory conditions for \(0\leq t\leq 1\) and \(-\infty< u_k<+\infty\), \(k=1,\dots, n\).
Mathematics Subject Classification ID: 34B15
zbMATH DE Number: 2182867
zbMATH Keywords: Carathéodory conditions
zbMATH Keywords: fixed-point theorem
zbMATH Keywords: completely continuous operator
MaRDI profile type: Publication
full work available at URL: b:joth.0000026293.71675.6f
OpenAlex ID: W2016014849
DOI: 10.1023/B:JOTH.0000026293.71675.6F
description: scientific article; zbMATH DE number 2182867