Existence results for delay second order differential inclusions

Azzam-Laouir, Dalila ; Haddad, Tahar

Discussiones Mathematicae. Differential Inclusions, Control and Optimization, Tome 28 (2008) no. 1, pp. 133-146.

Résumé

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.

Détail

Keywords: boundary-value problems, delay differential inclusions, fixed point, retract

Bibliographie

[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.

[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.

[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.

[4] C. Castaing, Quelques applications du Théorème de Banach-Dieudonné à l'intégration, Preprint 67, Université de Montpellier II.

[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.

[6] C. Castaing and A.G. Ibrahim, Functional differential inclusions on closed sets in Banach spaces, Adv. Math. Econ 2 (2000), 21-39.

[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.

[8] C. Castaing, A. Salvadori and L. Thibault, Functional evolution equations governed by nonconvex sweeping process, J. Nonlin. Conv. Anal. 2 (2001), 217-241.

[9] C. Castaing and M. Valadier, Convex Analysis and Measurable Multifunctions, Springer-Verlag, Berlin, 1977.

[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.

[11] A. Fryszkowski, Fixed Point Theory for Decomposable Sets, Topological Fixed Point Theory and Its Applications, 2004. Kluwer Academic Publishers, Dordrecht.

[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.

[13] A.G. Ibrahim, On differential inclusions with memory in Banach spaces, Proc. Math. Phys. Soc. Egypt 67 (1992), 1-26.

[14] P. Hartman, Ordinary Differenial Equations, John Wiley and Sons, New York, London, Sydney, 1967.

[15] S. Hu and N.S. Papageorgiou, Handbook of Multivalued Analysis, Vol. I: Theory, Kluwer, Dordrecht, The Netherlands, 1997.

[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.

[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.

[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.

[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.