ASYMPTOTIC BEHAVIOR OF FUNCTIONAL DYNAMIC EQUATIONS IN TIME SCALE

TitleASYMPTOTIC BEHAVIOR OF FUNCTIONAL DYNAMIC EQUATIONS IN TIME SCALE
Publication TypeJournal Article
Year of Publication2010
AuthorsCASTILLO SAMUEL, PINTO MANUEL
JournalDynamic Systems and Applications
Volume19
Start Page165
Pagination13
Date Published2010
ISSN1056-2176
AMS Subject Classification39A10
Abstract

It is considered a scalar linear functional dynamic equation in time scale with delayed argument of the form

(0.1)                                                           y(t) = b(t) y( τ(t) ), t ∈ T ∩ [0, +∞]

where T, the time scale, is a closed subset of R without upper bound for this case, is de Hilger’s derivate, which among other things, unifies difference operator for sequences and the derivate. The functions b, τ : T → C, τ > 0, are “locally integrable” and satisfy integral smallness conditions in a sense to be defined later. Asymptotic formulas of solutions of equation (0.1) are given. They unify and extend asymptotic formulas of difference and differential equations.

PDFhttps://acadsol.eu/dsa/articles/19/12-DSA-229.pdf
Refereed DesignationRefereed