On a nonlinear ordinary differential equation
type: Item
instance of: scholarly article
title: On a nonlinear ordinary differential equation
zbMATH Open document ID: 0828.34017
DOI: 10.1007/BF02112473
author: P. E. Zhidkov
author: V. Zh. Sakbaev
published in: Mathematical Notes
publication date: 1995-07-10T00:00:00Z
review text: The authors consider the nonlinear boundary-value problem on the half- line (1) \(y''+ {N- 1\over x} y'= f(y)\), \(x> 0\), \(y'(0)= y(+\infty)= 0\), where \(f\) is a smooth function, \(f'(0)> 0\), \(N> 1\), and establish a theorem on the existence of solutions with any number of roots for the case when \(f(y)\) is an odd function which satisfies the condition \(\lim_{y\to \infty} {f(y)\over y}= \lambda\leq 0\) and has exactly one positive root. A great bibliography of papers where problem (1) is considered is given in this paper.
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 34A34
zbMATH DE Number: 771967
Wikidata QID: Q115392743
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 771967