On positive solutions of boundary value problems for second-order functional differential equations on infinite intervals.
type: Item
instance of: scholarly article
title: On positive solutions of boundary value problems for second-order functional differential equations on infinite intervals.
zbMATH Open document ID: 1036.34075
DOI: 10.1016/S0022-247X(03)00246-4
author: Chuanzhi Bai
author: Jin-Xuan Fang
published in: Journal of Mathematical Analysis and Applications
publication date: 2003-07-30T00:00:00Z
review text: The authors study the functional boundary value problem \[ \begin{gathered} x''(t)- px'(t)- qx(t)+ f(t, x_t, x_t')= 0,\quad t\geq 0,\\ \alpha x(t)-\beta x'(t)= \xi(t),\quad -\tau\leq t\leq t0,\quad \lim_{t\to\infty}\, x(t)= 0,\end{gathered} \] with \(p,\alpha,\beta\in [0,\infty)\), \(\alpha^2+ \beta^2> 0\), \(q> 0\) and \(x_t(\theta)= x(t+ \theta)\) for \(\theta\in [-\tau, 0]\). They give conditions for the existence of positive solutions to the above problem. Existence results are proved by a fixed-point theorem on cones.
Mathematics Subject Classification ID: 34K10
zbMATH DE Number: 1957244
zbMATH Keywords: functional-differential equation
zbMATH Keywords: boundary value problem
zbMATH Keywords: positive solutions
reviewed by: Svatoslav Staněk
MaRDI profile type: Publication
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full work available at URL: s0022-247x(03)00246-4
OpenAlex ID: W1990095581
description: scientific article; zbMATH DE number 1957244