Properties of the set of positive solutions to Dirichlet boundary value problems with time singularities

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F13%3A33144737" target="_blank" >RIV/61989592:15310/13:33144737 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.2478/s11533-013-0324-7" target="_blank" >http://dx.doi.org/10.2478/s11533-013-0324-7</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.2478/s11533-012-0047-1" target="_blank" >10.2478/s11533-012-0047-1</a>

Result language
angličtina
Original language name
Properties of the set of positive solutions to Dirichlet boundary value problems with time singularities
Original language description
The paper investigates the structure and properties of the set S of all positive solutions to a singular Dirichlet boundary value problem on the interval [0,T]. It is shown that for each non-negative c there exists a nonempty and compact set Sc of positive solutions whose derivative at T is equal to -c. The uniqueness of the problem is discussed. Having a special case of the problem, we introduce an ordering in S showing that the difference of any two solutions of Sc keeps its sign on [0,T]. The application on an equation with blow-up solutions is given here.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Publication year
2013
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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