Eventually positive and bounded solutions of even-order nonlinear neutral differential equations

摘要

Consider the even-order nonlinear neutral differential equation [a(t)x(t) - Sigma(m)(i=1) b(i)(t)x(t-tau(i))]((n)) - Sigma(l)(j=1) p(j) (t)f(j) (t, x(t-sigma(j))) = 0, t >= 0, and the associated differential inequality [a(t)x(t) - Sigma(m)(i=1) b(i)(t)x(t-tau(i))]((n)) - Sigma(l)(j=1) p(j) (t)f(j) (t, x(t-sigma(j))) >= 0, t >= 0 Using Lebesgue's dominated convergence theorem, a necessary and sufficient condition for the existence of eventually positive and bounded solutions is obtained. (C) 2008 Elsevier Ltd. All rights reserved.