| Title:
|
Existence of nonnegative periodic solutions in neutral integro-differential equations with functional delay (English) |
| Author:
|
Soulahia, Imene |
| Author:
|
Ardjouni, Abdelouaheb |
| Author:
|
Djoudi, Ahcene |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
56 |
| Issue:
|
1 |
| Year:
|
2015 |
| Pages:
|
23-44 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The fixed point theorem of Krasnoselskii and the concept of large contractions are employed to show the existence of a periodic solution of a nonlinear integro-differential equation with variable delay \begin{equation*} x'(t)= -\int_{t-\tau (t)}^{t}a(t,s) g(x(s))\,ds + \frac{d}{dt}Q (t,x(t-\tau (t)))+ G(t,x(t),x(t-\tau (t))). \end{equation*} We transform this equation and then invert it to obtain a sum of two mappings one of which is completely continuous and the other is a large contraction. We choose suitable conditions for $\tau $, $g$, $a$, $Q$ and $G$ to show that this sum of mappings fits into the framework of a modification of Krasnoselskii's theorem so that existence of nonnegative T-periodic solutions is concluded. (English) |
| Keyword:
|
Krasnoselskii's fixed points |
| Keyword:
|
periodic solution |
| Keyword:
|
large contraction |
| MSC:
|
34K20 |
| MSC:
|
34K30 |
| MSC:
|
34K40 |
| idZBL:
|
Zbl 06433803 |
| idMR:
|
MR3311575 |
| DOI:
|
10.14712/1213-7243.015.103 |
| . |
| Date available:
|
2015-03-10T17:33:26Z |
| Last updated:
|
2017-04-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144186 |
| . |
| Reference:
|
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