Geodesic
Asymptotic behavior of solutions of neutral nonlinear differential equations
Archivum mathematicum, Tome 38 (2002) no. 4, pp. 319-325

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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 \[ u^{\prime \prime }+f(t,u)=0\,. \]
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 \[ u^{\prime \prime }+f(t,u)=0\,. \]
Classification : 34K11, 34K25, 34K40
Keywords: neutral equation; asymptotic behavior 
Džurina, Jozef. Asymptotic behavior of solutions of neutral nonlinear differential equations. Archivum mathematicum, Tome 38 (2002) no. 4, pp. 319-325. http://geodesic.mathdoc.fr/item/ARM_2002_38_4_a8/
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     title = {Asymptotic behavior of solutions of neutral nonlinear differential equations},
     journal = {Archivum mathematicum},
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     zbl = {1090.34053},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_2002_38_4_a8/}
}
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