h-Stability for Differential Systems Relative to Initial Time Difference

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h-Stability for Differential Systems Relative to Initial Time Difference

and Applied Analysis 3 Moreover, using the condition (iii), we obtain z (t) ≤ h (t) h −1 (τ 0 ) ( 󵄩󵄩󵄩󵄩y0 − x0 󵄩󵄩󵄩󵄩 + 󵄨󵄨󵄨󵄨η 󵄨󵄨󵄨󵄨) . (12) Then from (12), we get 󵄩󵄩󵄩󵄩x (t, τ0, y0) − x (t − η, t0, x0) 󵄩󵄩󵄩󵄩 ≤ [ 󵄩󵄩󵄩󵄩y0 − x0 󵄩󵄩󵄩󵄩 + 󵄨󵄨󵄨󵄨τ0 − t0 󵄨󵄨󵄨󵄨] h (t) h −1 (τ 0 ) . (13) So by Definition 1 with c = 1, the solution x(t, τ 0 , y 0 ) of (2) is ITDhS with respect to the solution x(t − η, t 0 , x 0 ). T...

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ژورنال

عنوان ژورنال: Abstract and Applied Analysis

سال: 2013

ISSN: 1085-3375,1687-0409

DOI: 10.1155/2013/827482