Existence of solutions to the first-order nonlinear boundary value problems
type: Item
instance of: scholarly article
title: Existence of solutions to the first-order nonlinear boundary value problems
zbMATH Open document ID: 1223.34033
author: Wei Ding
author: Yepeng Xing
published in: Taiwanese Journal of Mathematics
publication date: 2011-05-06T00:00:00Z
review text: The authors consider the boundary value problem for impulsive system of differential equations of first order \[ \begin{aligned} &x'(t) = f(t,x(t)),\quad t \in (0,T), \;t \neq t_k,\\ &\Delta x(t_k) = I_k(x(t_k)),\;k = 1,\dots,m,\\ &ax(0) + x(T) = b, \end{aligned} \] where \(0 < t_1 < \dots < t_m < T\), \(f : [0,T]\times {\mathbb R}\to {\mathbb R}\), \(I_k : {\mathbb R} \to {\mathbb R}\) are continuous, \(a\), \(b \in {\mathbb R}\). Existence results for various special cases of this BVP are obtained. As the main tool there is used Schaefer is fixed a point theorem and the nonlinear alternative.
reviewed by: Jan Tomeček
Mathematics Subject Classification ID: 34B37
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 47N20
zbMATH DE Number: 5885183
zbMATH Keywords: boundary value problem
zbMATH Keywords: linear boundary conditions
zbMATH Keywords: system of differential equations
zbMATH Keywords: first order
zbMATH Keywords: Schaefer fixed point theorem
zbMATH Keywords: existence
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.11650/twjm/1500405969
OpenAlex ID: W4239026956
DOI: 10.11650/TWJM/1500405969
description: scientific article; zbMATH DE number 5885183