In this paper, some fixed point principle is applied to prove the existence of solutions for delay second order differential inclusions with three-point boundary conditions in the context of a separable Banach space. A topological property of the solutions set is also established.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1098, author = {Dalila Azzam-Laouir and Tahar Haddad}, title = {Existence results for delay second order differential inclusions}, journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization}, volume = {28}, year = {2008}, pages = {133-146}, zbl = {1188.34080}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1098} }
Dalila Azzam-Laouir; Tahar Haddad. Existence results for delay second order differential inclusions. Discussiones Mathematicae, Differential Inclusions, Control and Optimization, Tome 28 (2008) pp. 133-146. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1098/
[000] [1] D. Azzam-Laouir, C. Castaing and L. Thibault, Three point boundary value problems for second order differential inclusions in Banach spaces, Control and Cybernetics 31 (3) (2002), 659-693. | Zbl 1111.34303
[001] [2] F.S. De Blasi and G. Pianigiani, Solutions sets of boundary value problems for nonconvex differential inclusions, Topol. Methods Nonlinear Anal. 2 (1993), 303-313. | Zbl 0785.34018
[002] [3] A. Bressan, A. Cellina and A. Fryszkowski, A case of absolute retracts in spaces of integrable functions, Proc. Amer. Math. Soc. 112 (1991), 413-418. | Zbl 0747.34014
[003] [4] C. Castaing, Quelques applications du Théorème de Banach-Dieudonné à l'intégration, Preprint 67, Université de Montpellier II.
[004] [5] C. Castaing, Quelques résultats de compacité liés à l'intégration, Colloque Anal. Fonct. (parution originelle) (1971), Bull. Soc. Math. France 31-32 (1972), 73-81.
[005] [6] C. Castaing and A.G. Ibrahim, Functional differential inclusions on closed sets in Banach spaces, Adv. Math. Econ 2 (2000), 21-39. | Zbl 0962.47031
[006] [7] C. Castaing and M.D.P. Monteiro Marques, Topological properties of solutions sets for sweeping process with delay, Portugaliae Mathematica 54 (4) (1997), 485-507.
[007] [8] C. Castaing, A. Salvadori and L. Thibault, Functional evolution equations governed by nonconvex sweeping process, J. Nonlin. Conv. Anal. 2 (2001), 217-241. | Zbl 0999.34062
[008] [9] C. Castaing and M. Valadier, Convex Analysis and Measurable Multifunctions, Springer-Verlag, Berlin, 1977.
[009] [10] P.W. Eloe, Y.N. Raffoul and C.C. Tisdell, Existence, uniqueness and constructive results for delay differential equations, Electronic Journal of Differential Equations 2005 (121) (2005), 1-11.
[010] [11] A. Fryszkowski, Fixed Point Theory for Decomposable Sets, Topological Fixed Point Theory and Its Applications, 2004. Kluwer Academic Publishers, Dordrecht. | Zbl 1086.47004
[011] [12] A.M. Gomaa, On the solutions sets of three-points boundary value problems for nonconvex differential inclusions, J. Egypt. Math. Soc. 12 (2) (2004), 97-107. | Zbl 1089.34011
[012] [13] A.G. Ibrahim, On differential inclusions with memory in Banach spaces, Proc. Math. Phys. Soc. Egypt 67 (1992), 1-26. | Zbl 0837.34024
[013] [14] P. Hartman, Ordinary Differenial Equations, John Wiley and Sons, New York, London, Sydney, 1967.
[014] [15] S. Hu and N.S. Papageorgiou, Handbook of Multivalued Analysis, Vol. I: Theory, Kluwer, Dordrecht, The Netherlands, 1997. | Zbl 0887.47001
[015] [16] N.S. Papageorgiou and V. Staicu, The method of upper-lower solutions for nonlinear second order differential inclusions, Nonlinear Anal. 67 (3) (2007), 708-726. | Zbl 1122.34008
[016] [17] N.S. Papageorgiou and N. Yannakakis, Second order nonlinear evolution inclusions, II. Structure of the solution set, Acta Math. Sin. (Engl. Ser.) 22 (1) (2006), 195-206. | Zbl 1109.34044
[017] [18] N.S. Papageorgiou and N. Yannakakis, Second order nonlinear evolution inclusions, I. Existence and relaxation results, Acta Math. Sin. (Engl. Ser.) 21 (5) (2005), 977-996. | Zbl 1095.34039
[018] [19] B. Ricceri, Une propriété topologique de l'ensemble des points fixes d'une contraction multivoque à valeurs convexes, Atti. Accad. Lincci. Fis. Mat. Natur. 81 (8) (1987), 283-286. | Zbl 0666.47030