Geodesic
Asymptotic behavior of solutions of neutral nonlinear differential equations
Archivum mathematicum, Tome 38 (2002) no. 4, pp. 319-325 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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 
@article{ARM_2002_38_4_a8,
     author = {D\v{z}urina, Jozef},
     title = {Asymptotic behavior of solutions of neutral nonlinear differential equations},
     journal = {Archivum mathematicum},
     pages = {319--325},
     year = {2002},
     volume = {38},
     number = {4},
     mrnumber = {1942662},
     zbl = {1090.34053},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_2002_38_4_a8/}
}
TY  - JOUR
AU  - Džurina, Jozef
TI  - Asymptotic behavior of solutions of neutral nonlinear differential equations
JO  - Archivum mathematicum
PY  - 2002
SP  - 319
EP  - 325
VL  - 38
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/ARM_2002_38_4_a8/
LA  - en
ID  - ARM_2002_38_4_a8
ER  - 
%0 Journal Article
%A Džurina, Jozef
%T Asymptotic behavior of solutions of neutral nonlinear differential equations
%J Archivum mathematicum
%D 2002
%P 319-325
%V 38
%N 4
%U http://geodesic.mathdoc.fr/item/ARM_2002_38_4_a8/
%G en
%F ARM_2002_38_4_a8
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/