Uniqueness of large solutions for non-monotone nonlinearities
type: Item
instance of: scholarly article
title: Uniqueness of large solutions for non-monotone nonlinearities
zbMATH Open document ID: 1415.34055
author: Julián López-Gómez
author: Luis Maire
published in: Nonlinear Analysis. Real World Applications
publication date: 2019-02-27T00:00:00Z
review text: The paper is concerned with the autonomous nonlinear second-order differential equation: \[ u''=f(u),\quad 0\leq t<T \] with the condition \(u'(0)=0\). More precisely, the authors investigate the existence and uniqueness of a large solution, i.e., a positive solution that explodes at the time \(T\): \(u(T)=+\infty\). The authors starts by estimating the maximum interval of existence and its bound \(T_{\max}\) by proving important properties of \(T_{\max}\). With further assumptions on \(T_{\max}\) together with \(f(0)=0\), \(f(u)>0\), \(f'(u)\geq 0\) for positive \(u\), existence and uniqueness of a large solution (among others) is established. The originality of the paper resides in that no monotonicity assumption on the nonlinearity \(f\) is required.
Mathematics Subject Classification ID: 34B18
zbMATH DE Number: 7030184
zbMATH Keywords: large positive solutions
zbMATH Keywords: uniqueness
zbMATH Keywords: multiplicity
zbMATH Keywords: dynamical approach
reviewed by: Smail Djebali
MaRDI profile type: Publication
full work available at URL: j.nonrwa.2018.11.003
OpenAlex ID: W2903488900
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Wikidata QID: Q128848461
DOI: 10.1016/J.NONRWA.2018.11.003
description: scientific article; zbMATH DE number 7030184