Functional differential equations of second order
type: Item
instance of: scholarly article
title: Functional differential equations of second order
zbMATH Open document ID: 1045.34037
published in: Bulletin of the Belgian Mathematical Society - Simon Stevin
publication date: 2004-02-02T00:00:00Z
review text: The existence of a unique solution of boundary-value problems for functional-differential equations of the form \[ x' (t)=f(t,x_t), \quad t\in[0,1],\qquad x(0)=\phi_0,\quad x(1)=k_1, \tag{*} \] is considered in this paper where \(\phi_0\in C_0=C([-\tau ,0],\mathbb R),\) \(\tau>0\) and \(f\in C([0,1]\times C_0,\mathbb R)\), and for \(t\in [0,1]\), \(x_t\in C_0\) is defined by \(x_t(s)=x(t+s)\), \(s\in [-\tau ,0]\). Two monotone sequences are constructed which, under certain conditions, converge to the unique solution of (\(*\)). This convergence is superlinear. Examples are given to illustrate the results obtained.
Mathematics Subject Classification ID: 34K10
Mathematics Subject Classification ID: 34A45
zbMATH DE Number: 2031047
zbMATH Keywords: boundary value problem
zbMATH Keywords: functional-differential equations
zbMATH Keywords: existence and uniqueness of solutions
author: Tadeusz Jankowski
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 2031047