Boundary value problems for second-order differential equations on unbounded domains in a Banach space.
type: Item
instance of: scholarly article
title: Boundary value problems for second-order differential equations on unbounded domains in a Banach space.
zbMATH Open document ID: 1035.34015
DOI: 10.1016/S0096-3003(02)00070-X
author: Yansheng Liu
published in: Applied Mathematics and Computation
publication date: 2003-01-28T00:00:00Z
review text: The author studies the following two-point boundary value problem for a second-order nonlinear differential equation in a Banach space \(X\) \[ \frac{d^2 x}{dt^2}=f \biggl(t, x(t), \frac{d x(t)}{dt}\biggr),\quad t\geq 0, \qquad x(t)=x_0, \quad \frac{d x(\infty)}{dt}=y_\infty, \] where \(x_0, y_\infty\in X\) are given vectors, and \(f: [0,\infty)\times X\times X\to X\) is a given continuous function. By virtue of the Sadovskii fixed-point theorem, the existence of solutions is investigated. Besides, the Lipschitz condition for \(f\) is not required.
Mathematics Subject Classification ID: 34B40
Mathematics Subject Classification ID: 34B20
zbMATH DE Number: 1861367
zbMATH Keywords: boundary value problem
zbMATH Keywords: fixed-point theorem
zbMATH Keywords: noncompactness measure
reviewed by: Michael I. Gil'
MaRDI profile type: Publication
cites work: Boundary value problems for impulsive integro-differential equations on unbounded domains in a Banach space
cites work: Q3904867
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description: scientific article; zbMATH DE number 1861367