MATHEMATICA, Tome 49 (72), N o 1, 2007, pp. 21–28 EXISTENCE OF VIABLE SOLUTIONS FOR A CLASS OF NONCONVEX DIFFERENTIAL INCLUSIONS WITH MEMORY AURELIAN CERNEA and VASILE LUPULESCU Abstract. We prove the existence of viable solutions for an autonomus differ- ential inclusion with memory in the case when the multifunction that define the inclusion is upper semicontinuous compact valued and contained in the Fr´ echet subdifferential of a φ-convex function of order two. MSC 2000. 34A60. Key words. Differential inclusion with memory, φ-convex function of order two, viable solutions. REFERENCES [1] Aubin, J.P. and Cellina, A., Differential inclusions, Springer, Berlin, 1984. [2] Br´ ezis, H., Analyse Functionelle, Th´ eorie et Applications, Masson, Paris, 1983. [3] Cardinali, T., Colombo, G., Papalini, F. and Tosques, M., On a class of evolution equations without convexity, Nonlinear Anal., 28 (1996), 217–234. [4] Cernea, A., Existence of viable solutions for a class of nonconvex differential inclu- sions, Math. Reports, 6(56) (2004), 217–224. [5] Cernea, A. and Lupulescu, V., Viable solutions for a class of nonconvex functional differential inclusions, Math. Reports, 7(57) (2005), 91–103. [6] Degiovanni, M., Marino, A. and Tosques, M., Evolution equations with lack of convexity, Nonlinear Anal., 9 (1995), 1401–1443. [7] Gavioli, A. and Malaguti, L., Viable solutions of differential inclusions with memory in Banach spaces, Portugal. Math., 57(2) (2000), 203–217. [8] Haddad, G., Monotone trajectories of differential inclusions and functional differential inclusions with memory, Israel J. Math., 39 (1981), 83–100. [9] Haddad, G., Monotone trajectories for functional differential inclusions, J. Diff. Equa- tions., 42 (1981), 1–24. [10] Lakshmikantham, V. and Leela, S., Nonlinear differential equations in abstract spaces, Pergamon Press, Oxford, 1981. Received September 29, 2005 Faculty of Mathematics and Informatics University of Bucharest Str. Academiei 14 RO-010014 Bucharest, Romania e-mail: acernea@math.math.unibuc.ro Departament of Mathematics “Constantin Brˆ ancu¸ si” University Str. Republicii 1 RO-210152 Tˆ argu Jiu, Romania e-mail: vasile@utgjiu.ro