Journal of Applied Mathematics and Stochastic Analysis 
Volume 6 (1993), Issue 1, Pages 55-68
doi:10.1155/S1048953393000061

Positive solutions of integrodifferential equations

Ch. G. Philos

 University of Ioannina, Department of Mathematics, P.O. Box 1186, Ioannina 451 I0, Greece
Received 1 January 1992; Revised 1 October 1992

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.