Affiliation:
1. Department of Mathematics , Ben Gurion University of the Negev , P.O. Box 653, Beer-Sheva 84105 , Israel
Abstract
Abstract
Let Bj
(t) (j = 1,..., m) and B(t, τ) (t ≥ 0, 0 ≤ τ ≤ 1) be bounded variable operators in a Banach space. We consider the equation
u
′
(
t
)
=
∑
k
=
1
m
B
k
(
t
)
u
(
t
-
h
k
(
t
)
)
+
∫
0
1
B
(
t
,
τ
)
u
(
t
-
h
0
(
τ
)
)
d
τ
(
t
≥
0
)
,
u'\left( t \right) = \sum\limits_{k = 1}^m {{B_k}\left( t \right)u\left( {t - {h_k}\left( t \right)} \right)} + \int\limits_0^1 {B\left( {t,\tau } \right)u\left( {t - {h_0}\left( \tau \right)} \right)d\tau \,\,\,\,\left( {t \ge 0} \right),}
where hk
(t) (t ≥ 0; k = 1, ..., m) and h
0(τ) are continuous nonnegative bounded functions. Explicit delay-dependent exponential stability conditions for that equation are established. Applications to integro-differential equations with delay are also discussed
Subject
Applied Mathematics,Numerical Analysis,Statistics and Probability,Analysis
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