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dc.contributor.authorBurkotová, Jana
dc.contributor.authorRachůnková, Irena
dc.contributor.authorRohleder, Martin
dc.contributor.authorStryja, Jakub
dc.date.accessioned2017-01-25T08:29:11Z
dc.date.available2017-01-25T08:29:11Z
dc.date.issued2016
dc.identifier.citationElectronic Journal of Qualitative Theory of Differential Equations. 2016, no. 121, p. 1-28.cs
dc.identifier.issn1417-3875
dc.identifier.urihttp://hdl.handle.net/10084/116818
dc.description.abstractWe study analytical properties of a singular nonlinear ordinary differential equation with a phi-Laplacian. In particular we investigate solutions of the initial value problem (p(t)phi(u'(t)))' + p(t)f(phi(u(t))) = 0, u(0) = u(0) is an element of [L-0, L], u'(0) = 0 on the half-line [0, infinity). Here, f is a continuous function with three zeros phi(L0) < 0 < phi(L), function p is positive on (0, infinity) and the problem is singular in the sense that p(0) - 0 and 1/p(t) may not be integrable on [0,1]. The main goal of the paper is to prove the existence of damped solutions defined as solutions u satisfying sup{u(t), t is an element of [0, infinity)} < L. Moreover, we study the uniqueness of damped solutions. Since the standard approach based on the Lipschitz property is not applicable here in general, the problem is more challenging. We also discuss the uniqueness of other types of solutions.cs
dc.format.extent564270 bytes
dc.format.mimetypeapplication/pdf
dc.language.isoencs
dc.publisherBolyai Institute, University of Szeged and the Hungarian Academy of Sciencescs
dc.relation.ispartofseriesElectronic Journal of Qualitative Theory of Differential Equationscs
dc.relation.urihttp://dx.doi.org/10.14232/ejqtde.2016.1.121cs
dc.subjectsecond order ODEcs
dc.subjecttime singularitycs
dc.subjectexistence and uniquenesscs
dc.subjectf -Laplaciancs
dc.subjectdamped solutioncs
dc.subjecthalf-linecs
dc.titleExistence and uniqueness of damped solutions of singular IVPs with phi-Laplaciancs
dc.typearticlecs
dc.identifier.doi10.14232/ejqtde.2016.1.121
dc.rights.accessopenAccess
dc.type.versionpublishedVersioncs
dc.type.statusPeer-reviewedcs
dc.description.sourceWeb of Sciencecs
dc.description.issue121cs
dc.description.lastpage28cs
dc.description.firstpage1cs
dc.identifier.wos000390898000001


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