Linearized oscillation theory for a nonlinear equation with a distributed delay

We obtain linearized oscillation theorems for the equation with distributed delays. (x)overdot(t) + Sigma(m)(k=1) r(k)(t) integral(t)(-infinity) f(k)(x(s)) d(s)R(k)(t, s) = 0. The results are applied to logistic, Lasota-Wazewska and Nicholson's blowflies equations with a distributed delay. In addition, the "Mean Value Theorem" is proved which claims that a solution of (1) also satisfies the linear equation with a variable concentrated delay. (x)overdot(t) + (Sigma(m)(k=1) r(k)(t)f'(k)(xi(k)(t))) x(g(t)) = 0. (C) 2007 Elsevier Ltd. All rights reserved.