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Asymptotic behavior of increasing solutions to a system of n nonlinear differential equations
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SYSNO ASEP 0385126 Druh ASEP J - Článek v odborném periodiku Zařazení RIV J - Článek v odborném periodiku Poddruh J Článek ve WOS Název Asymptotic behavior of increasing solutions to a system of n nonlinear differential equations Tvůrce(i) Řehák, Pavel (MU-W) RID, SAI, ORCID Zdroj.dok. Nonlinear Analysis: Theory, Methods & Applications. - : Elsevier - ISSN 0362-546X
Roč. 77, January 12 (2013), s. 45-58Poč.str. 14 s. Jazyk dok. eng - angličtina Země vyd. GB - Velká Británie Klíč. slova oncreasing solution ; asymptotic formula ; quasilinear system Vědní obor RIV BA - Obecná matematika Institucionální podpora MU-W - RVO:67985840 UT WOS 000310502900003 EID SCOPUS 84867900963 DOI https://doi.org/10.1016/j.na.2012.08.019 Anotace 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. Pracoviště Matematický ústav Kontakt Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Rok sběru 2013
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