Bounded Solutions of Some Abstract Differential Equations

descriptionPublicationkeyboard_double_arrow_right Article , Other literature type 01 Nov 1969Publisher:JSTORJournal:Proceedings of the American Mathematical Society, volume 23, page 340 (issn: 0002-9939,

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Authors: Zaidman, S.;

doi: 10.2307/2037169 , 10.1090/s0002-9939-1969-0245953-2

Bounded Solutions of Some Abstract Differential Equations

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Abstract

there followAs the existence of a sequence (tn)r -oo, such that SUPn;N Czu(tn)1x to, the function u(t) admits the representation u(t) = T(t-to)u(to). Also, a well-known fact is that (Xo-A)-1T(t) = T(t)(Xo-A)-1. Let us put now: w(t) = (Xo-A)-lu(t); obviously sequence {Io(tn) }l contains a convergent subsequence C0(tn)jCX, and co(t) = T(t-to)0(to), Vt_to. Let tE(00, 00) be fixed and ko big enough to get tnk ko. Then we obtain, as t > trt ,

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