| Title:
|
The monotone iterative technique for periodic boundary value problems of second order impulsive differential equations (English) |
| Author:
|
Liz, E. |
| Author:
|
Nieto, Juan J. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
34 |
| Issue:
|
3 |
| Year:
|
1993 |
| Pages:
|
405-411 |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper, we develop monotone iterative technique to obtain the extremal solutions of a second order periodic boundary value problem (PBVP) with impulsive effects. We present a maximum principle for ``impulsive functions'' and then we use it to develop the monotone iterative method. Finally, we consider the monotone iterates as orbits of a (discrete) dynamical system. (English) |
| Keyword:
|
impulsive differential equations |
| Keyword:
|
periodic boundary value problem |
| Keyword:
|
monotone iterative technique |
| MSC:
|
34A37 |
| MSC:
|
34A45 |
| MSC:
|
34B15 |
| MSC:
|
34C25 |
| MSC:
|
34D45 |
| idZBL:
|
Zbl 0780.34006 |
| idMR:
|
MR1243071 |
| . |
| Date available:
|
2009-01-08T18:04:40Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118596 |
| . |
| Reference:
|
[1] Cabada A., Nieto J.J.: A generalization of the monotone iterative technique for nonlinear second order periodic boundary value problems.J. Math. Anal. Appl. 151 (1990), 181-189. Zbl 0719.34039, MR 1069454 |
| Reference:
|
[2] Hale J.: Theory of functional differential equations.Springer-Verlag, New York, 1977. Zbl 1092.34500, MR 0508721 |
| Reference:
|
[3] Lakshmikantham V., Bainov D.D., Simeonov P.S.: Theory of impulsive differential equations.World Scientific, Singapore, 1989. Zbl 0719.34002, MR 1082551 |
| Reference:
|
[4] Hu S., Lakshmikantham V.: Periodic boundary value problems for second order impulsive differential systems.Nonlinear Anal. 13 (1989), 75-85. Zbl 0712.34033, MR 0973370 |
| Reference:
|
[5] Ladde G.S., Lakshmikantham V., Vatsala A.S.: Monotone iterative techniques for nonlinear differential equations.Pitman Advanced Publishing Program, 1985. Zbl 0658.35003, MR 0855240 |
| Reference:
|
[6] Liu X.: Nonlinear boundary value problems for first order impulsive integro-differential equations.Applicable Anal. 36 (1989), 119-130. Zbl 0688.45015, MR 1040882 |
| Reference:
|
[7] Liz E., Nieto J.J.: Periodic solutions of discontinuous impulsive differential systems.J. Math. Anal. Appl. 161 (1991), 388-394. Zbl 0753.34027, MR 1132115 |
| Reference:
|
[8] Nieto J.J.: Nonlinear second order periodic boundary value problems with Carathéodory functions.Applicable Anal. 34 (1989), 111-128. Zbl 0662.34022, MR 0926825 |
| . |
