# Existence results for delay second order differential inclusions

Dalila Azzam-Laouir; Tahar Haddad

Discussiones Mathematicae, Differential Inclusions, Control and Optimization (2008)

- Volume: 28, Issue: 1, page 133-146
- ISSN: 1509-9407

## Access Full Article

top## Abstract

top## How to cite

topDalila Azzam-Laouir, and Tahar Haddad. "Existence results for delay second order differential inclusions." Discussiones Mathematicae, Differential Inclusions, Control and Optimization 28.1 (2008): 133-146. <http://eudml.org/doc/271176>.

@article{DalilaAzzam2008,

abstract = {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.},

author = {Dalila Azzam-Laouir, Tahar Haddad},

journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},

keywords = {boundary-value problems; delay differential inclusions; fixed point; retract},

language = {eng},

number = {1},

pages = {133-146},

title = {Existence results for delay second order differential inclusions},

url = {http://eudml.org/doc/271176},

volume = {28},

year = {2008},

}

TY - JOUR

AU - Dalila Azzam-Laouir

AU - Tahar Haddad

TI - Existence results for delay second order differential inclusions

JO - Discussiones Mathematicae, Differential Inclusions, Control and Optimization

PY - 2008

VL - 28

IS - 1

SP - 133

EP - 146

AB - 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.

LA - eng

KW - boundary-value problems; delay differential inclusions; fixed point; retract

UR - http://eudml.org/doc/271176

ER -

## References

top- [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. Zbl1111.34303
- [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. Zbl0785.34018
- [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. Zbl0747.34014
- [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. Zbl0962.47031
- [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. Zbl0999.34062
- [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. Zbl1086.47004
- [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. Zbl1089.34011
- [13] A.G. Ibrahim, On differential inclusions with memory in Banach spaces, Proc. Math. Phys. Soc. Egypt 67 (1992), 1-26. Zbl0837.34024
- [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. Zbl0887.47001
- [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. Zbl1122.34008
- [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. Zbl1109.34044
- [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. Zbl1095.34039
- [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. Zbl0666.47030

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.