| Title:
|
Existence of periodic solutions for first-order totally nonlinear neutral differential equations with variable delay (English) |
| Author:
|
Ardjouni, Abdelouaheb |
| Author:
|
Djoudi, Ahcène |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
55 |
| Issue:
|
2 |
| Year:
|
2014 |
| Pages:
|
215-225 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We use a modification of Krasnoselskii's fixed point theorem due to Burton (see [Liapunov functionals, fixed points and stability by Krasnoselskii's theorem, Nonlinear Stud. 9 (2002), 181--190], Theorem 3) to show that the totally nonlinear neutral differential equation with variable delay \begin{equation*} x'(t) = -a(t)h (x(t)) + c(t)x'(t-g(t))Q' (x(t-g(t))) + G (t,x(t),x(t-g(t))), \end{equation*} has a periodic solution. We invert this equation to construct a fixed point mapping expressed as a sum of two mappings such that one is compact and the other is a large contraction. We show that the mapping fits very nicely for applying the modification of Krasnoselskii's theorem so that periodic solutions exist. (English) |
| Keyword:
|
periodic solution |
| Keyword:
|
nonlinear neutral differential equation |
| Keyword:
|
large contraction |
| Keyword:
|
integral equation |
| MSC:
|
34K13 |
| MSC:
|
34K20 |
| MSC:
|
34K40 |
| MSC:
|
45D05 |
| MSC:
|
45J05 |
| idZBL:
|
Zbl 06391539 |
| idMR:
|
MR3193927 |
| . |
| Date available:
|
2014-06-07T15:37:59Z |
| Last updated:
|
2016-07-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143803 |
| . |
| 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:
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| Reference:
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| Reference:
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| Reference:
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