Discussiones Mathematicae Differential Inclusions, Control and Optimization 34 (2014 ) 61–62 doi:10.7151/dmdico.1159 DELAY PERTURBED EVOLUTION PROBLEMS INVOLVING TIME DEPENDENT SUBDIFFERENTIAL OPERATORS Soumia Sa¨ ıdi and Mustapha Fateh Yarou Laboratoire LMPA, Department of Mathematics Jijel University, Algeria e-mail: soumiass@hotmail.fr mfyarou@yahoo.com Abstract We investigate in the present paper, the existence and uniqueness of solutions for functional differential inclusions involving a subdifferential op- erator in the infinite dimensional setting. The perturbation which contains the delay is single-valued, separately measurable, and separately Lipschitz. We prove, without any compactness condition, that the problem has one and only one solution. Keywords: Differential inclusions, subdifferential operator, Lipschitz func- tions, set-valued map, delay, perturbation, absolutely continuous map. 2010 Mathematics Subject Classification: 34A60, 34K09, 49A52. References [1] J.P. Aubin and A. Celina, Differential Inclusions, Set-valued Maps and Viability Theory (Springer-Verlag Berlin Heidelberg, 1984). doi:10.1007/978-3-642-69512-4 [2] H. Benabdellah, C. Castaing and A. Salvadori, Compactness and discretization methods for differential inclusions and evolution problems, Atti. Sem. Math. Fis. Univ. Modena XLV (1997) 9–51. [3] M. Bounkhel and M. Yarou, Existence results for first and second order nonconvex sweeping process with delay, Port. Math. 61 (2) (2004) 2007–2030. [4] H. Br´ ezis, Op´ erateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert, Lecture Notes in Math. (North-Holland/American Elsevier, Amsterdam/New York, 1973). [5] C. Castaing, A.G. Ibrahim and M. Yarou, Existence problems in second order evo- lution inclusions: discretization and variational approach, Taiwanese J. Math. 12 (6) (2008) 1435–1477.