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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 792431, 9 pages
Relaxation Problems Involving Second-Order Differential Inclusions
1Taibah University, Faculty of Applied Science, Department of Applied Mathematics, Al-Madinah, Saudi Arabia
2Mathematics Department, Faculty of Science, Helwan University, Cairo, Egypt
Received 12 November 2012; Accepted 12 March 2013
Academic Editor: Malisa R. Zizovic
Copyright © 2013 Adel Mahmoud Gomaa. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- A. M. Gomaa, Set-valued functions and set-valued differential equations [Ph.D. thesis], Faculty of Science, Cairo University, 1999.
- A. G. Ibrahim and A. M. Gomaa, “Existence theorems for a functional multivalued three-point boundary value problem of second order,” Journal of the Egyptian Mathematical Society, vol. 8, no. 2, pp. 155–168, 2000.
- A. G. Ibrahim and A. G. Gomaa, “Extremal solutions of classes of multivalued differential equations,” Applied Mathematics and Computation, vol. 136, no. 2-3, pp. 297–314, 2003.
- A. M. Gomaa, “On the solution sets of three-point boundary value problems for nonconvex differential inclusions,” Journal of the Egyptian Mathematical Society, vol. 12, no. 2, pp. 97–107, 2004.
- D. L. Azzam, C. Castaing, and L. Thibault, “Three boundary value problems for second order differential inclusions in Banach spaces,” Control and Cybernetics, vol. 31, no. 3, pp. 659–693, 2002.
- B. Satco, “Second order three boundary value problem in Banach spaces via Henstock and Henstock-Kurzweil-Pettis integral,” Journal of Mathematical Analysis and Applications, vol. 332, no. 2, pp. 919–933, 2007.
- P. Hartman, Ordinary Differential Equations, John Wiley and Sons, New York, NY, USA, 1964.
- A. M. Gomaa, “On the solution sets of four-point boundary value problems for nonconvex differential inclusions,” International Journal of Geometric Methods in Modern Physics, vol. 8, no. 1, pp. 23–37, 2011.
- A. M. Gomaa, “On four-point boundary value problems for differential inclusions and differential equations with and without multivalued moving constraints,” Czechoslovak Mathematical Journal, vol. 62, no. 137, pp. 139–154, 2012.
- C. J. Himmelberg and F. S. Van Vleck, “Selection and implicit function theorems for multifunctions with Souslin graph,” Bulletin de l'Académie Polonaise des Sciences, vol. 19, pp. 911–916, 1971.
- C. J. Himmelberg and F. S. Van Vleck, “Some selection theorems for measurable functions,” Canadian Journal of Mathematics, vol. 21, pp. 394–399, 1969.
- C. J. Himmelberg and F. S. Van Vleck, “Extreme points of multifunctions,” Indiana University Mathematics Journal, vol. 22, pp. 719–729, 1973.
- K. Kuratowski and C. Ryll-Nardzewski, “A general theorem on selectors,” Bulletin de l'Académie Polonaise des Sciences, vol. 13, pp. 397–403, 1965.
- E. Klein and A. C. Thompson, Theory of Correspondences, John Wiley and Sons, New York, NY, USA, 1984.
- C. Castaing and M. Valadier, Convex Analysis and Measurable Multifunctions, vol. 580 of Lecture Notes in Mathematics, Springer, Berlin, Germany, 1977.
- J.-P. Aubin and A. Cellina, Differential Inclusions Set-Valued Maps and Viability Theory, vol. 264, Springer, Berlin, Germany, 1984.
- F. S. De Blasi and J. Myjak, “On continuous approximations for multifunctions,” Pacific Journal of Mathematics, vol. 123, no. 1, pp. 9–31, 1986.
- A. A. Tolstonogov, “Extremal selectors of multivalued mappings and the “bang-bang” principle for evolution inclusions,” Bulletin de l'Académie Polonaise des Sciences, Série des Sciences Mathématiques, vol. 317, no. 3, pp. 589–593, 1991.
- D. Kravvaritis and N. S. Papageorgiou, “Boundary value problems for nonconvex differential inclusions,” Journal of Mathematical Analysis and Applications, vol. 185, no. 1, pp. 146–160, 1994.
- S. R. Bernfeld and V. Lakshmikantham, An Introduction to Nonlinear Boundary Value, Academic Press, New York, NY, USA, 1974.
- A. G. Ibrahim and A. M. Gomaa, “Topological properties of the solution sets of some differential inclusions,” Pure Mathematics and Applications, vol. 10, no. 2, pp. 197–223, 1999.
- A. Bressan and G. Colombo, “Extensions and selections of maps with decomposable values,” Studia Mathematica, vol. 90, no. 1, pp. 69–86, 1988.
- N. S. Papageorgiou, “On measurable multifunctions with applications to random multivalued equations,” Mathematica Japonica, vol. 32, no. 3, pp. 437–464, 1987.
- M. Benamara, Point Extrémaux, Multi-applications et Fonctionelles Intégrales [M.S. thesis], Université de Grenoble, 1975.
- N. S. Papageorgiou, “Convergence theorems for Banach space valued integrable multifunctions,” International Journal of Mathematics and Mathematical Sciences, vol. 10, no. 3, pp. 433–442, 1987.
- L. X. Truong, L. T. P. Ngoc, and N. T. Long, “Positive solutions for an -point boundary-value problem,” Electronic Journal of Differential Equations, vol. 2008, no. 111, 10 pages, 2008.