| Title:
|
A survey and some new results on the existence of solutions of IPBVPs for first order functional differential equations (English) |
| Author:
|
Liu, Yuji |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
54 |
| Issue:
|
6 |
| Year:
|
2009 |
| Pages:
|
527-549 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
This paper deals with the periodic boundary value problem for nonlinear impulsive functional differential equation $$ \begin{cases} x'(t)=f(t,x(t),x(\alpha _1(t)),\cdots ,x(\alpha _n(t))) \text {for a.e.} \ t\in [0,T], \Delta x(t_k)=I_k(x(t_k)), \ k=1,\cdots ,m, x(0)=x(T). \end{cases} $$ We first present a survey and then obtain new sufficient conditions for the existence of at least one solution by using Mawhin's continuation theorem. Examples are presented to illustrate the main results. (English) |
| Keyword:
|
periodic boundary value problem |
| Keyword:
|
impulsive differential equation |
| Keyword:
|
fixed-point theorem |
| Keyword:
|
growth condition |
| MSC:
|
34B10 |
| MSC:
|
34B15 |
| MSC:
|
34K10 |
| MSC:
|
34K45 |
| MSC:
|
47N20 |
| idZBL:
|
Zbl 1212.34184 |
| idMR:
|
MR2563123 |
| DOI:
|
10.1007/s10492-009-0032-6 |
| . |
| Date available:
|
2010-07-20T13:27:28Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140382 |
| . |
| Reference:
|
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| Reference:
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