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Asymptotic behavior of increasing solutions to a system of n nonlinear differential equations
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SYSNO ASEP 0385126 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title Asymptotic behavior of increasing solutions to a system of n nonlinear differential equations Author(s) Řehák, Pavel (MU-W) RID, SAI, ORCID Source Title Nonlinear Analysis: Theory, Methods & Applications. - : Elsevier - ISSN 0362-546X
Roč. 77, January 12 (2013), s. 45-58Number of pages 14 s. Language eng - English Country GB - United Kingdom Keywords oncreasing solution ; asymptotic formula ; quasilinear system Subject RIV BA - General Mathematics Institutional support MU-W - RVO:67985840 UT WOS 000310502900003 EID SCOPUS 84867900963 DOI https://doi.org/10.1016/j.na.2012.08.019 Annotation 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, as special 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. Workplace Mathematical Institute Contact Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Year of Publishing 2013
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