Positive solutions of integrodifferential equations

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.