A topological approach to superlinear indefinite boundary value problems
type: Item
instance of: scholarly article
title: A topological approach to superlinear indefinite boundary value problems
zbMATH Open document ID: 0990.34019
DOI: 10.12775/TMNA.2000.017
author: Duccio Papini
author: Fabio Zanolin
published in: Topological Methods in Nonlinear Analysis
publication date: 2002-08-02T00:00:00Z
review text: Some boundary value problems are considered for the differential equation \(\ddot x + q(t)g(x) = 0\), where \(g(x)\) has superlinear growth at infinity and \(q(t)\) changes sign. It is shown, that there exist solutions with a prescribed number of zeroes in each interval of positivity of \(q(t)\). Moreover, for each interval of negativity, one can arbitrarily specify in advance that the solution has exactly one zero being also strictly monotone or that it has no zeroes and exactly one zero of the first derivative is in this interval. Various generalizations are discussed.
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 34C10
Mathematics Subject Classification ID: 34C25
zbMATH DE Number: 1545373
zbMATH Keywords: superlinear boundary value problems
zbMATH Keywords: zeroes of solutions
reviewed by: Sergei A. Brykalov
MaRDI profile type: Publication
full work available at URL: tmna.2000.017
OpenAlex ID: W2169669205
description: scientific article; zbMATH DE number 1545373