| Title:
|
Study of Stability in Nonlinear Neutral Differential Equations with Variable Delay Using Krasnoselskii–Burton’s Fixed Point (English) |
| Author:
|
MESMOULI, Mouataz Billah |
| Author:
|
Ardjouni, Abdelouaheb |
| Author:
|
Djoudi, Ahcene |
| Language:
|
English |
| Journal:
|
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica |
| ISSN:
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0231-9721 |
| Volume:
|
55 |
| Issue:
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2 |
| Year:
|
2016 |
| Pages:
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129-142 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper, we use a modification of Krasnoselskii’s fixed point theorem introduced by Burton (see [Burton, T. A.: Liapunov functionals, fixed points and stability by Krasnoseskii’s theorem. Nonlinear Stud., 9 (2002), 181–190.] Theorem 3) to obtain stability results of the zero solution of the totally nonlinear neutral differential equation with variable delay \[ x^{\prime }\left( t\right) =-a\left( t\right) h\left( x\left( t\right) \right) +\frac{d}{dt}Q\left( t,x\left( t-\tau \left( t\right) \right) \right) +G\left( t,x\left( t\right) ,x\left( t-\tau \left( t\right) \right) \right) . \] The stability of the zero solution of this eqution provided that $h\left(0\right) =Q\left( t,0\right) =G\left( t,0,0\right) =0$. The Caratheodory condition is used for the functions $Q$ and $G$. (English) |
| Keyword:
|
Fixed point |
| Keyword:
|
stability |
| Keyword:
|
delay |
| Keyword:
|
stability |
| Keyword:
|
nonlinear neutral equation |
| Keyword:
|
large contraction mapping |
| Keyword:
|
integral equation |
| MSC:
|
34K20 |
| MSC:
|
34K30 |
| MSC:
|
34K40 |
| MSC:
|
47H10 |
| idZBL:
|
Zbl 06724368 |
| . |
| Date available:
|
2017-03-16T12:52:05Z |
| Last updated:
|
2018-01-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/146066 |
| . |
| Reference:
|
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| Reference:
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| Reference:
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