Asymptotic behavior of nonoscillatory solutions to n-th order nonlinear neutral differential equations

Abstract

For a class of n-th order nonlinear neutral differential equations, sufficient conditions for all nonoscillatory solutions to satisfy lim(t) (->+infinity) t(1-n)x(t) = a are established. For another class of equations, necessary and sufficient conditions for nonoscillatory solutions to satisfy the above condition are obtained. Our theorems complement and extend recent results reported in the literature. (c) 2007 Elsevier Ltd. All rights reserved.