In this paper we study asymptotic behavior of solutions of second order neutral functional differential equation of the form \[ \Big (x(t)+px(t-\tau )\Big )^{\prime \prime }+f(t,x(t))=0\,. \] We present conditions under which all nonoscillatory solutions are asymptotic to $at+b$ as $t\rightarrow \infty $, with $a,b\in R$. The obtained results extend those that are known for equation \[ u^{\prime \prime }+f(t,u)=0\,. \]
@article{107846,
author = {Jozef D\v zurina},
title = {Asymptotic behavior of solutions of neutral nonlinear differential equations},
journal = {Archivum Mathematicum},
volume = {038},
year = {2002},
pages = {319-325},
zbl = {1090.34053},
mrnumber = {1942662},
language = {en},
url = {http://dml.mathdoc.fr/item/107846}
}
Džurina, Jozef. Asymptotic behavior of solutions of neutral nonlinear differential equations. Archivum Mathematicum, Tome 038 (2002) pp. 319-325. http://gdmltest.u-ga.fr/item/107846/
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