Journal of Applied Mathematics and Stochastic Analysis
Volume 6 (1993), Issue 1, Pages 55-68
doi:10.1155/S1048953393000061
Positive solutions of integrodifferential equations
University of Ioannina, Department of Mathematics, P.O. Box 1186, Ioannina 451 I0, Greece
Received 1 January 1992; Revised 1 October 1992
Copyright © 1993 Ch. G. Philos. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
Integrodifferential equations of the forms
x′(t)+p(t)∫0tK(t−s)x(s)ds=0 and x′(t)+q(t)∫−∞tK(t−s)x(s)ds=0
are considered, where K∈C([0,∞),[0,∞)), p∈C([0,∞),[0,∞)) and
q∈C((−∞,∞),[0,∞)). Necessary conditions and also sufficient
conditions for the existence of positive solutions are established.