Existence of solution of \(m\)-point boundary value problems of second-order differential systems with impulses
type: Item
instance of: scholarly article
title: Existence of solution of \(m\)-point boundary value problems of second-order differential systems with impulses
zbMATH Open document ID: 1032.34024
DOI: 10.1016/S0096-3003(00)00110-7
author: Bing Liu
author: Jianshe Yu
published in: Applied Mathematics and Computation
publication date: 2003-01-28T00:00:00Z
review text: Here, the authors study the existence of solutions to the following \(m\)-point boundary value problem for second-order differential equations with impulses \[ \begin{aligned} (\rho'(t)x'(t))' &=f(t,x(t),x'(t)),\quad t \in [0,1], t \neq t_i,\\ x(t_i^+) - x(t_i^-) &= I_i(x(t_i),x'(t_i)),\quad i =1,\dots,k,\\ x'(t_i^+) - x'(t_i^-) &= J_i(x(t_i),x'(t_i)),\quad i =1,\dots,k,\\ x'(0)&=0,\qquad x(1)=\sum_{j=1}^{m-2}a_jx(\eta_j). \end{aligned} \] where \(\rho:[0,1]\to \mathbb{R}\) is a positive continuous differentiable function, \(f: [0,1]\times \mathbb{R}^n\times \mathbb{R}^n\to \mathbb{R}^n,\) \(I_i, J_i: \mathbb{R}^n\times \mathbb{R}^n\to \mathbb{R}^n\) are continuous, \(k\) is a fixed positive integer, \(t_i\), \(i=1,2,\ldots,k\), are fixed points with \(0<t_1<t_2<\ldots<t_k<1,\) \(\eta_j\in (0,1)\), \(j=1,2,\ldots,m-2\), be given \(0<\eta_1<\eta_2<\ldots<\eta_{m-2}<1,\) \(\eta_j\neq t_i,\) and \(a_j, j=1,2,\ldots, m-2\), are nonnegative real constant numbers. The coincidence degree continuation theorem and the concept of autonomous curvature bound set are used.
reviewed by: Sotiris K. Ntouyas
Mathematics Subject Classification ID: 34B37
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 47N20
zbMATH DE Number: 1860987
zbMATH Keywords: Multi-point boundary value problems
zbMATH Keywords: Coincidence degree theory
zbMATH Keywords: Impulsive
MaRDI profile type: Publication
cites work: Q3995625
cites work: Existence of solutions of boundary value problems for nonlinear second order impulsive differential equations in Banach spaces
cites work: Multiple positive solutions of boundary-value problems for impulsive differential equations
cites work: Periodic boundary value problems for second order impulsive integrodifferential equations of mixed type in Banach spaces
cites work: Periodic boundary value problems for impulsive integro-differential equations of mixed type in Banach spaces
cites work: Boundary value problems for impulsive integro-differential equations on unbounded domains in a Banach space
cites work: Periodic solutions for second order impulsive differential systems
cites work: Coincidence degree, and nonlinear differential equations
cites work: Q3820939
cites work: Solvability of an \(m\)-point boundary value problem for second order ordinary differential equations
cites work: Solvability of three point boundary value problems at resonance
cites work: Solvability of \(m\)-point boundary value problems with nonlinear growth
cites work: Q3140332
Recommended article: Solvability of second-order \(m\)-point boundary value problems with impulses
Recommended article: Q3610304
Recommended article: Q5390129
Recommended article: Existence of solutions to boundary value problems for impulsive second order differential inclusions
Recommended article: Existence results for boundary value problems of second order impulsive differential equations
Recommended article: Q3153436
Recommended article: Q3630813
Recommended article: Solutions of second-order \(m\)-point boundary value problems for impulsive dynamic equations on time scales
Recommended article: Existence and nonexistence of positive solutions for the second-order m-point eigenvalue impulsive boundary value problem
Recommended article: Q5017399
description: scientific article; zbMATH DE number 1860987