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

Result code in 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>
Alternative codes found
RIV/00216224:14410/13:00065974
Result on the web
<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>

Result language
angličtina
Original language name
Asymptotic behavior of increasing solutions to a system of n nonlinear differential equations
Original language description
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.
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/GAP201%2F10%2F1032" target="_blank" >GAP201/10/1032: Difference equations and dynamic equations on time scales III</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2013
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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