Oscillatory solutions of singular equations arising in hydrodynamics
type: Item
instance of: scholarly article
title: Oscillatory solutions of singular equations arising in hydrodynamics
zbMATH Open document ID: 1203.34058
DOI: 10.1155/2010/872160
author: Irena Rachůnková
author: Jan Tomeček
author: Jakub Stryja
published in: Advances in Difference Equations
publication date: 2010-06-25T00:00:00Z
review text: Motivated by the recent papers of the first two authors [Math. Comput. Modelling 51, No.~5--6, 658--669 (2010; Zbl 1190.34029), and Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 72, No.~3--4 (A), 2114--2118 (2010; Zbl 1186.34014)], the initial value problem for the second order nonlinear differential equation \[ (p(t)u')'=p(t)f(u),\quad t\in [0,\infty), \tag{\(*\)} \] is investigated. The functions \(p,f\) satisfy certain restrictions which imply, among others, that \(t=0\) is a singular point of the investigated equation. One of the main results of the paper gives additional conditions on the nonlinearity \(f\) under which the singular initial value problem associated with \((*)\) has oscillatory solutions with decreasing amplitudes.
reviewed by: Ondřej Došlý
Mathematics Subject Classification ID: 34C10
Mathematics Subject Classification ID: 34A12
zbMATH DE Number: 5726185
zbMATH Keywords: singular initial value problem
zbMATH Keywords: oscillatory solution
zbMATH Keywords: damped solution
Wikidata QID: Q59249875
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2010/872160
OpenAlex ID: W2055948396
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description: scientific article; zbMATH DE number 5726185