| Title:
|
Asymptotic behavior of solutions of neutral nonlinear differential equations (English) |
| Author:
|
Džurina, Jozef |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
38 |
| Issue:
|
4 |
| Year:
|
2002 |
| Pages:
|
319-325 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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 \[ u^{\prime \prime }+f(t,u)=0\,. \] (English) |
| Keyword:
|
neutral equation |
| Keyword:
|
asymptotic behavior |
| MSC:
|
34K11 |
| MSC:
|
34K25 |
| MSC:
|
34K40 |
| idZBL:
|
Zbl 1090.34053 |
| idMR:
|
MR1942662 |
| . |
| Date available:
|
2008-06-06T22:31:11Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107846 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
[7] Rogovchenko, Y. V., Villari, G.: Asymptotic behavior of solutions for second order nonlinear autonomous differential equations.NoDEA- Nonlinear Differential Equations Appl. 4 (1997), 271–282. MR 1446220 |
| Reference:
|
[8] Tong, J.: The asymptotic behavior of a class of nonlinear differential equations second order.Proc. Amer. Math. Soc. 84 (1982), 235–236. MR 0637175 |
| . |
