Existence of solutions to the state dependent sweeping process with delay

Volume 7, Issue 2, pp 70--77 http://dx.doi.org/10.22436/jnsa.007.02.01

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Authors

Touma Haddad - Département de Mathématique, Faculté des Sciences Exactes et Informatique, Université de Jijel, B.P.98, Algérie. Tahar Haddad - Laboratoire LMPA, Département de Mathématiques, Faculté des Sciences Exactes et Informatique, Université de Jijel, B.P.98, Algérie.

Abstract

In this paper, we prove, via new projection algorithm, the existence of solutions for functional differential inclusion governed by state dependent sweeping process with perturbation depending on all variables and with delay.

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Keywords

• functional differential inclusion
• normal cone
• sweeping process
• perturbation
• delay.

MSC

•  35K22
•  34A60

References

• [1] J. P. Aubin, A. Cellina, Differential Inclusions , Springer-Verlag, Berlin (1984)


• [2] C. Castaing, P. Raynaud de Fitte, M. Valadier, Young measures on topological spaces, With applications in control theory and probability theory, Kluwer Academic publisher, (2004),


• [3] C. Castaing, T. Haddad, A. Salvadory, A variational convergence problem with antiperiodic boundary conditions, Pacific journal of optimization, 6 (2010), 153-176.


• [4] C. Castaing, A. G. Ibrahim, M. Yarou, Some contributions to nonconvex sweeping process, J. Nonlinear Convex Anal., 10 (2009), 1-20.


• [5] C. Castaing, A. Jofre, A. Salvadory, Control problems governed by functional evolution inclusions with Young measures, J. Nonlinear Convex Anal., 5 (2004), 131-152.


• [6] C. Castaing, A. Salvadory, L Thibault , Functional evolution equations governed by nonconvex sweeping process, J. Nonlinear Convex Anal., 2 (2001), 217-241.


• [7] C. Castaing, M. Valadier, Convex Analysis and Measurable multifunctions, Lecture Notes on Math. 580, Springer Verlag, Berlin (1977)


• [8] J. F. Edmond, A. L. Thibault , Relaxiation and optimal control problem involving a perturbed sweeping process, Math. program, Ser. B, 104 (2005), 347-373.


• [9] T. Haddad, A. Jourani, L. Thibault, Reduction of sweeping process to unconstrained differential inclusion, Pacific Journal of Optimization., 4 (2008), 493-512.


• [10] C. Henry, An existence result for a class of differential equation with multivalued right-hand side, J. Math. Anal. Appl, 41 (1973), 1979-1986.


• [11] J. J. Moreau, Evolution problem associated with a moving convex set in a Hilbert space, J. Diff. Eqs, 26 (1977), 347-374.


• [12] M. D. P. Monteiro Marques, Differential inclusions in nonsmooths mechanical problems, Shokcks and dry Friction, , Progress in Nonlinear Differential Equations an Their Applications, Birkhauser. 9 (1993)