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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
Volume: 62
Issue: 1
Year: 2012
Pages: 139-154
Summary lang: English
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Category: math
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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.
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
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Date available: 2012-03-05T07:18:46Z
Last updated: 2014-04-07
Stable URL: http://hdl.handle.net/10338.dmlcz/142047
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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
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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: [12] Papageorgiou, N. S.: Convergence theorems for Banach space valued integrable multifunctions.Int. J. Math. Math. Sci. 10 (1987), 433-442. Zbl 0619.28009, MR 0896595, 10.1155/S0161171287000516
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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