Explicit integral criteria for the existence of positive solutions of the linear delayed equation $dot x(t) =-c(t)x(t-tau(t))$

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216305%3A26110%2F15%3APU114481" target="_blank" >RIV/00216305:26110/15:PU114481 - isvavai.cz</a>
Result on the web
<a href="http://www.sciencedirect.com/science/article/pii/S0893965913003455" target="_blank" >http://www.sciencedirect.com/science/article/pii/S0893965913003455</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.aml.2013.11.010" target="_blank" >10.1016/j.aml.2013.11.010</a>

Result language
angličtina
Original language name
Explicit integral criteria for the existence of positive solutions of the linear delayed equation $dot x(t) =-c(t)x(t-tau(t))$
Original language description
The paper analyses the linear differential equation with single delay $dot x(t)=-c(t)x(t-tau(t))$ with continuous $taucolon [t_0,infty)to (0,r]$, $r>0$, $t_0in bR$, and $ccolon [t_0-r,infty)to (0,infty)$. New explicit integral criteria for the existence of a positive solution expressed in terms of $c$ and $tau$ are derived, an overview of known relevant criteria is provided, and relevant comparisons are also given. It is demonstrated that the known criteria are consequences of the new results.
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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Project
<a href="/en/project/ED1.1.00%2F02.0068" target="_blank" >ED1.1.00/02.0068: Central european institute of technology</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>S - Specificky vyzkum na vysokych skolach

Publication year
2015
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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