Asymptotic behavior of increasing solutions to a system of n nonlinear differential equations

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F13%3A00385126" target="_blank" >RIV/67985840:_____/13:00385126 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/00216224:14410/13:00065974

Výsledek na webu

<a href="http://dx.doi.org/10.1016/j.na.2012.08.019" target="_blank" >http://dx.doi.org/10.1016/j.na.2012.08.019</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.na.2012.08.019" target="_blank" >10.1016/j.na.2012.08.019</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Asymptotic behavior of increasing solutions to a system of n nonlinear differential equations

Popis výsledku v původním jazyce

We consider the system x(i)' = a(i)(t)vertical bar x(i+1)vertical bar(alpha i)sgn x(i+1), i = 1, ... , n, n = 2, where ai, i = 1,..., n, are positive continuous functions on [a, infinity), alpha(i) is an element of (0, infinity), i = 1,..., n, with alpha(1) ... alpha(n) < 1, and x(n+1) means x(1). We analyze the asymptotic behavior of the solutions to this system whose components are eventually positive increasing. In particular, we derive exact asymptotic formulas for the extreme case, where all the solution components tend to infinity (the so-called strongly increasing solutions). We offer two approaches: one is based on the asymptotic equivalence theorem, and the other utilizes the theory of regular variation. The above-mentioned system includes, asspecial cases, two-term nonlinear scalar differential equations of arbitrary order n and systems of n/2 second-order nonlinear equations (provided n is even), which are related to elliptic partial differential systems.

Název v anglickém jazyce

Asymptotic behavior of increasing solutions to a system of n nonlinear differential equations

Popis výsledku anglicky

We consider the system x(i)' = a(i)(t)vertical bar x(i+1)vertical bar(alpha i)sgn x(i+1), i = 1, ... , n, n = 2, where ai, i = 1,..., n, are positive continuous functions on [a, infinity), alpha(i) is an element of (0, infinity), i = 1,..., n, with alpha(1) ... alpha(n) < 1, and x(n+1) means x(1). We analyze the asymptotic behavior of the solutions to this system whose components are eventually positive increasing. In particular, we derive exact asymptotic formulas for the extreme case, where all the solution components tend to infinity (the so-called strongly increasing solutions). We offer two approaches: one is based on the asymptotic equivalence theorem, and the other utilizes the theory of regular variation. The above-mentioned system includes, asspecial cases, two-term nonlinear scalar differential equations of arbitrary order n and systems of n/2 second-order nonlinear equations (provided n is even), which are related to elliptic partial differential systems.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

<a href="/cs/project/GAP201%2F10%2F1032" target="_blank" >GAP201/10/1032: Diferenční rovnice a dynamické rovnice na ,,time scales'' III</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2013

Kód důvěrnosti údajů

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

Název periodika

Nonlinear Analysis: Theory, Methods & Applications

ISSN

0362-546X

e-ISSN

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Svazek periodika

77

Číslo periodika v rámci svazku

Jan 12

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

14

Strana od-do

45-58

Kód UT WoS článku

000310502900003

EID výsledku v databázi Scopus

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