On four-point boundary value problems for differential inclusions and differential equations with and without multivalued moving constraints
Czechoslovak Mathematical Journal (2012)
- Volume: 62, Issue: 1, page 139-154
- ISSN: 0011-4642
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topGomaa, Adel Mahmoud. "On four-point boundary value problems for differential inclusions and differential equations with and without multivalued moving constraints." Czechoslovak Mathematical Journal 62.1 (2012): 139-154. <http://eudml.org/doc/247008>.
@article{Gomaa2012,
abstract = {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.},
author = {Gomaa, Adel Mahmoud},
journal = {Czechoslovak Mathematical Journal},
keywords = {differential equations; differential inclusions; multipoint boundary value problems; bang-bang controls; Green functions; differential equation; differential inclusion; multipoint boundary value problem; bang-bang controls; Green function},
language = {eng},
number = {1},
pages = {139-154},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On four-point boundary value problems for differential inclusions and differential equations with and without multivalued moving constraints},
url = {http://eudml.org/doc/247008},
volume = {62},
year = {2012},
}
TY - JOUR
AU - Gomaa, Adel Mahmoud
TI - On four-point boundary value problems for differential inclusions and differential equations with and without multivalued moving constraints
JO - Czechoslovak Mathematical Journal
PY - 2012
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 62
IS - 1
SP - 139
EP - 154
AB - 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.
LA - eng
KW - differential equations; differential inclusions; multipoint boundary value problems; bang-bang controls; Green functions; differential equation; differential inclusion; multipoint boundary value problem; bang-bang controls; Green function
UR - http://eudml.org/doc/247008
ER -
References
top- Aubin, J.-P., Cellina, A., Differential Inclusions. Set-Valued Maps and Viability Theory, Grundlehren der Mathematischen Wissenschaften, 264, Springer-Verlag, Berlin (1984). (1984) Zbl0538.34007MR0755330
- Benamara, M., "Point Extrémaux, Multi-applications et Fonctionelles Intégrales", Thése de 3éme Cycle, Université de Grenoble (1975). (1975)
- Bressan, A., Colombo, G., 10.4064/sm-90-1-69-86, Stud. Math. 90 (1988), 69-86. (1988) Zbl0677.54013MR0947921DOI10.4064/sm-90-1-69-86
- Brown, L. D., Purves, R., 10.1214/aos/1176342510, Ann. Stat. 1 (1973), 902-912. (1973) Zbl0265.28003MR0432846DOI10.1214/aos/1176342510
- Castaing, C., Valadier, M., 10.1007/BFb0087688, Lecture Notes in Mathematics, 580. Springer Verlag, Berlin-Heidelberg-New York (1977). (1977) Zbl0346.46038MR0467310DOI10.1007/BFb0087688
- Gomaa, A. M., 10.1142/S021988781100494X, Int. J. Geom. Methods Mod. Phys. 8 (2011), 23-37. (2011) Zbl1220.34021MR2782872DOI10.1142/S021988781100494X
- Gupta, Ch. P., 10.1016/0022-247X(92)90179-H, J. Math. Anal. Appl. 168 (1992), 540-551. (1992) Zbl0763.34009MR1176010DOI10.1016/0022-247X(92)90179-H
- Ibrahim, A. G., Gomaa, A. M., 10.1016/S0096-3003(02)00040-1, Appl. Math. Comput. 136 (2003), 297-314. (2003) Zbl1037.34052MR1937933DOI10.1016/S0096-3003(02)00040-1
- Klein, E., Thompson, A., Theory of Correspondences. Including Applications to Mathematical Economic, Canadian Mathematical Society Series of Monographs and Advanced Texts. A Wiley-Interscience Publication. New York, John Wiley & Sons (1984). (1984) MR0752692
- Marano, S. A., 10.1006/jmaa.1994.1158, J. Math. Anal. Appl. 183 (1994), 518-522. (1994) Zbl0801.34025MR1274852DOI10.1006/jmaa.1994.1158
- 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. (1991) Zbl0784.54024MR1121349
- Papageorgiou, N. S., 10.1155/S0161171287000516, Int. J. Math. Math. Sci. 10 (1987), 433-442. (1987) Zbl0619.28009MR0896595DOI10.1155/S0161171287000516
- Papageorgiou, N. S., Kravvaritis, D., 10.1006/jmaa.1994.1238, J. Math. Anal. Appl. 185 (1994), 146-160. (1994) Zbl0817.34009MR1283047DOI10.1006/jmaa.1994.1238
- Papageorgiou, N. S., On measurable multifunction with applications to random multivalued equations, Math. Jap. 32 (1987), 437-464. (1987) MR0914749
- Ricceri, O. N., Ricceri, B., 10.1080/00036819008839966, Appl. Anal. 38 (1990), 259-270. (1990) MR1116184DOI10.1080/00036819008839966
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