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Subexponential solutions of scalar linear integro-differential equations with delay

Appleby, John A.D. and Győri, 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) = − n Xi=1 aix(t − i) + Z t 0 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.

Item Type:Article (Published)
Uncontrolled Keywords:volterra integro–differential equations; subexponential function; exponential asymptotic stability;
Subjects:Mathematics > Differential equations
DCU Faculties and Centres:DCU Faculties and Schools > Faculty of Science and Health > School of Mathematical Sciences
Publisher:The Research Institute, The College of Judea and Samaria
Official URL:
Use License:This item is licensed under a Creative Commons Attribution-NonCommercial-Share Alike 3.0 License. View License
ID Code:18
Deposited On:26 Oct 2006 by DORAS Administrator. Last Modified 28 Nov 2016 14:08

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