Positive decreasing solutions of systems of second order singular differential equations
type: Item
instance of: scholarly article
title: Positive decreasing solutions of systems of second order singular differential equations
zbMATH Open document ID: 0972.34003
DOI: 10.1155/S1025583400000321
author: T. Tanigawa
author: Takaši Kusano
published in: Journal of Inequalities and Applications
publication date: 2001-11-13T00:00:00Z
full work available at URL: https://eudml.org/doc/121354
review text: Here, the singular differential systems \[ \bigl(p(t)|y' |^{\alpha-1} y'\bigr)'= \varphi(t)z^{-\lambda}, \quad\bigl(q(t)|z' |^{\beta-1} z'\bigr)'=\psi (t)y^{-\mu}, \tag{*} \] are considered, where \(\alpha, \beta,\lambda, \mu\) are positive constants in an interval \([a,\infty)\), and \(p,q,\varphi,\psi\) are positive continuous functions on \([a,\infty)\). A positive decreasing solution to system (*) is called singular according to whether it exists on \([a,\infty)\) or it ceases to exist at a finite point of \([a,\infty)\). First, conditions are given under which there does exist a singular solution to (*) and is called an extinct singular solution. Then conditions for the existence of proper solutions to system (*) are established. They are classified into moderately decreasing solutions and strongly decreasing solutions according to the rate of their decay as \(t\to\infty\) and called decreasing proper solutions. The basic results are presented in 5 theorems, and its significance is discovered in 3 examples. 2 remarkes and 3 applications.
Mathematics Subject Classification ID: 34A25
Mathematics Subject Classification ID: 34A34
Mathematics Subject Classification ID: 34D15
Mathematics Subject Classification ID: 34C11
zbMATH DE Number: 1563280
zbMATH Keywords: nonlinear differential equation
zbMATH Keywords: singular asymptotic solution
zbMATH Keywords: extinct singular solution
reviewed by: Gasanbek T. Arazov
MaRDI profile type: Publication
OpenAlex ID: W1979847968
description: scientific article; zbMATH DE number 1563280