Two classes of asymptotically different positive solutions to advanced differential equations via two different fixed-point principles

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Two classes of asymptotically different positive solutions to advanced differential equations via two different fixed-point principles

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Two classes of asymptotically different positive solutions to advanced differential equations via two different fixed-point principles

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

—

Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2017

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Mathematical Methods in the Applied Sciences

ISSN

0170-4214

e-ISSN

1099-1476

Svazek periodika

40

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

16

Strana od-do

1422-1437

Kód UT WoS článku

000397303100006

EID výsledku v databázi Scopus

2-s2.0-84994381519