Existence of positive solutions of the Liénard differential equation
type: Item
instance of: scholarly article
title: Existence of positive solutions of the Liénard differential equation
zbMATH Open document ID: 0778.34021
author: Daniela Hricišáková
published in: Journal of Mathematical Analysis and Applications
publication date: 1993-09-05T00:00:00Z
review text: Existence and qualitative properties are obtained for positive solutions \(x(t)\) of the Liénard-type differential equation (1) \(x''+f(x)x'+g(x)=0\), \(t\geq t_ 0\). In particular, conditions on \(f\), \(g\) are given for the existence of a positive solution such that \(0<x'(t)<1\), \(\lim_{t\to\infty}x(t)=+\infty\), and \(\lim_{t\to\infty}x'(t)<1\). Also, a positive decreasing solution is obtained with both \(x(t)\) and \(x'(t)\) decaying to zero at \(\infty\). Corollaries concern nonoscillatory properties and the nonexistence of periodic solutions.
Mathematics Subject Classification ID: 34C11
zbMATH DE Number: 399083
zbMATH Keywords: existence
zbMATH Keywords: qualitative properties
zbMATH Keywords: positive solutions
zbMATH Keywords: Liénard-type differential equation
zbMATH Keywords: nonoscillatory properties
zbMATH Keywords: nonexistence of periodic solutions
reviewed by: Charles A. Swanson
MaRDI profile type: Publication
full work available at URL: jmaa.1993.1230
OpenAlex ID: W1981228354
Wikidata QID: Q115395443
DOI: 10.1006/JMAA.1993.1230
description: scientific article; zbMATH DE number 399083