Two classes of asymptotically different positive solutions to advanced differential equations via two different fixed-point principles
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216305%3A26220%2F17%3APU123880" target="_blank" >RIV/00216305:26220/17:PU123880 - isvavai.cz</a>
Result on the web
<a href="http://onlinelibrary.wiley.com/doi/10.1002/mma.4064/full" target="_blank" >http://onlinelibrary.wiley.com/doi/10.1002/mma.4064/full</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1002/mma.4064" target="_blank" >10.1002/mma.4064</a>
Alternative languages
Result language
angličtina
Original language name
Two classes of asymptotically different positive solutions to advanced differential equations via two different fixed-point principles
Original language description
The paper considers a system of advanced-type functional differential equations $$ dot{x}(t) = F(t,x^t) $$ where $F$ is a given functional, $x^t in C([0,r],{mathbb R}^n)$, $r>0$ and $x^t(theta)=x(t+theta)$, $theta in [0,r]$. Two different results on the existence of solutions, with coordinates bounded above and below by the coordinates of the given vector functions if $ttoinfty$, are proved using two different fixed-point principles. It is illustrated by examples that, applying both results simultaneously to the same equation yields two positive solutions asymptotically different for $ttoinfty$. The equation $$ dot{x}(t) = left(a+{b}/{t}right),x(t+tau) $$ where $a, tau in (0,infty)$, $a<1/(taue)$, $b in {mathbb R}$ are constants can serve as a linear example. The existence of a pair of positive solutions asymptotically different for $ttoinfty$ is proved and their asymptotic behavior is investigated. The results are also illustrated by a nonlinear equation.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10102 - Applied mathematics
Result continuities
Project
—
Continuities
S - Specificky vyzkum na vysokych skolach
Others
Publication year
2017
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Mathematical Methods in the Applied Sciences
ISSN
0170-4214
e-ISSN
1099-1476
Volume of the periodical
40
Issue of the periodical within the volume
3
Country of publishing house
GB - UNITED KINGDOM
Number of pages
16
Pages from-to
1422-1437
UT code for WoS article
000397303100006
EID of the result in the Scopus database
2-s2.0-84994381519