Subexponential solutions of scalar linear integro-differential equations with delay
Appleby, John A.D. and Gyori, István and Reynolds, David W. (2004) Subexponential solutions of scalar linear integro-differential equations with delay. Functional DIfferential Equations, 11 (1-2). pp. 11-18.
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This paper considers the asymptotic behaviour of solutions of the scalar
linear convolution integro-differential equation with delay
x0(t) = −
aix(t − i) + Z t
k(t − s)x(s) ds, t > 0,
x(t) = (t), − t 0,
where = max1in i. In this problem, k is a non-negative function in L1(0,1)\C[0,1),
i 0, ai > 0 and is a continuous function on [−, 0]. The kernel k is subexponential
in the sense that limt!1 k(t)(t)−1 > 0 where is a positive subexponential function. A
consequence of this is that k(t)et ! 1 as t ! 1 for every > 0.
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