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On omega-limit sets of ordinary differential equations in Banach spaces
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SYSNO ASEP 0352543 Druh ASEP J - Článek v odborném periodiku Zařazení RIV J - Článek v odborném periodiku Poddruh J Článek ve WOS Název On omega-limit sets of ordinary differential equations in Banach spaces Tvůrce(i) Hájek, Petr Pavel (MU-W) RID, SAI
Vivi, P. (CZ)Zdroj.dok. Journal of Mathematical Analysis and Applications. - : Elsevier - ISSN 0022-247X
Roč. 371, č. 2 (2010), s. 793-812Poč.str. 20 s. Jazyk dok. eng - angličtina Země vyd. US - Spojené státy americké Klíč. slova omega-limit set ; ODE in Banach space Vědní obor RIV BA - Obecná matematika CEP IAA100190801 GA AV ČR - Akademie věd CEZ AV0Z10190503 - MU-W (2005-2011) UT WOS 000280566900039 EID SCOPUS 77955269904 DOI 10.1016/j.jmaa.2010.05.059 Anotace Let X be an infinite-dimensional real Banach space. We classify omega-limit sets of autonomous ordinary differential equations x' = f(x), x(0) = x(0), where f : X -> X is Lipschitz, as being of three types I-III. We denote by S-x the class of all sets in X which are omega-limit sets of a solution to (1), for some Lipschitz vector field f and some initial condition x(0) is an element of X. We say that S is an element of S-x is of type I if there exists a Lipschitz function integral and a solution x such that S = Omega(x) and {x(t): t >= 0} boolean AND S = empty set. We say that S is an element of S-x is of type II if it has nonempty interior. We say that S is an element of S-x is of type III if it has empty interior and for every solution x (of Eq. (1) where f is Lipschitz) such that S = Omega(x) it holds {x(t). t >= 0} subset of S. Pracoviště Matematický ústav Kontakt Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Rok sběru 2011
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