| Title:
|
On four-point boundary value problems for differential inclusions and differential equations with and without multivalued moving constraints (English) |
| Author:
|
Gomaa, Adel Mahmoud |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
62 |
| Issue:
|
1 |
| Year:
|
2012 |
| Pages:
|
139-154 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We deal with the problems of four boundary points conditions for both differential inclusions and differential equations with and without moving constraints. Using a very recent result we prove existence of generalized solutions for some differential inclusions and some differential equations with moving constraints. The results obtained improve the recent results obtained by Papageorgiou and Ibrahim-Gomaa. Also by means of a rather different approach based on an existence theorem due to O. N. Ricceri and B. Ricceri we prove existence results improving earlier theorems by Gupta and Marano. (English) |
| Keyword:
|
differential equations |
| Keyword:
|
differential inclusions |
| Keyword:
|
multipoint boundary value problems |
| Keyword:
|
bang-bang controls |
| Keyword:
|
Green functions |
| MSC:
|
05C35 |
| MSC:
|
34A60 |
| MSC:
|
34B05 |
| MSC:
|
34B27 |
| MSC:
|
49J30 |
| idZBL:
|
Zbl 1249.34053 |
| idMR:
|
MR2899741 |
| DOI:
|
10.1007/s10587-012-0002-0 |
| . |
| Date available:
|
2012-03-05T07:18:46Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/142047 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
[3] Bressan, A., Colombo, G.: Extensions and selections of maps with decomposable values.Stud. Math. 90 (1988), 69-86. Zbl 0677.54013, MR 0947921, 10.4064/sm-90-1-69-86 |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
[7] Gupta, Ch. P.: Solvability of a three-point nonlinear boundary value problem for a second order ordinary differential equation.J. Math. Anal. Appl. 168 (1992), 540-551. Zbl 0763.34009, MR 1176010, 10.1016/0022-247X(92)90179-H |
| Reference:
|
[8] Ibrahim, A. G., Gomaa, A. M.: Extremal solutions of classes of multivalued differential equations.Appl. Math. Comput. 136 (2003), 297-314. Zbl 1037.34052, MR 1937933, 10.1016/S0096-3003(02)00040-1 |
| Reference:
|
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| Reference:
|
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| Reference:
|
[11] Tolstonogov, A. A.: Extremal selections of multivalued mappings and the "bang-bang" principle for evolution inclusions.Sov. Math. Dokl. 43 (1991), 481-485 Translation from Dokl. Akad. Nauk SSSR 317 (1991), 589-593. Zbl 0784.54024, MR 1121349 |
| Reference:
|
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| Reference:
|
[13] Papageorgiou, N. S., Kravvaritis, D.: Boundary value problems for nonconvex differential inclusions.J. Math. Anal. Appl. 185 (1994), 146-160. Zbl 0817.34009, MR 1283047, 10.1006/jmaa.1994.1238 |
| Reference:
|
[14] Papageorgiou, N. S.: On measurable multifunction with applications to random multivalued equations.Math. Jap. 32 (1987), 437-464. MR 0914749 |
| Reference:
|
[15] Ricceri, O. N., Ricceri, B.: An existence theorem for inclusions of the type $\Psi (u)(t) \in F(t, \Phi (u)(t))$ and an application to a multivalued boundary value problem.Appl. Anal. 38 (1990), 259-270. MR 1116184, 10.1080/00036819008839966 |
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