The asymptotic behavior of nonoscillatory solutions of some nonlinear differential equations
type: Item
instance of: scholarly article
title: The asymptotic behavior of nonoscillatory solutions of some nonlinear differential equations
zbMATH Open document ID: 0967.34044
DOI: 10.1016/S0362-546X(99)00132-7
author: Ć. Ljubović
author: Mustafa R. S. Kulenovic
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2001-08-20T00:00:00Z
review text: The authors deal with the differential equation \[ (r(t)g(y'(t)))'-p(t)f(y(t))=0,\quad t\geq t_0 \tag{1} \] with continuous and sufficiently smooth functions \(r, g, p\) and \(f\). By a solution to (1) it is meant a function \(y \in C^1([t_0,\infty),\mathbb{R})\) such that \(r(t)g(y'(t))\) is differentiable and \(y\) satisfies (1) for all \(t\geq t_0\). The authors study the asymptotic behavior of the so-called extremal solutions and they give their characterization in four theorems. This extends earlier results concerning the asymptotic behavior of solutions of special cases to (1) contained in the works listed in references of the paper under review. Further, using the fixed-point theorem on ordered sets by \textit{A. Tarski} [Pac. J. Math. 5, 285-309 (1955; Zbl 0064.26004)], the authors prove the existence and estimates of nonextremal solutions to (1). Illustrated examples are shown here, as well.
reviewed by: Irena Rachůnková
Mathematics Subject Classification ID: 34D05
Mathematics Subject Classification ID: 34C10
Mathematics Subject Classification ID: 34C11
Mathematics Subject Classification ID: 34A34
zbMATH DE Number: 1513298
zbMATH Keywords: asymptotic behavior
zbMATH Keywords: nonoscillatory solutions
zbMATH Keywords: nonlinear differential equations
MaRDI profile type: Publication
cites work: Q5554555
cites work: Q4750126
cites work: Oscillation and non-oscillation theorems for a class of second order quasilinear differential equations
cites work: Q3708392
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full work available at URL: s0362-546x(99)00132-7
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description: scientific article; zbMATH DE number 1513298