Nonlinear Analysis 50 (2002) 1025–1034 www.elsevier.com/locate/na Existence of solutions to a class of evolution inclusions  Aurelian Cernea a , Vasile Staicu b; ∗ a Faculty of Mathematics, University of Bucharest, Academiei 14, 70109 Bucharest, Romania b Department of Mathematics, Aveiro University, 3810-193 Aveiro, Portugal Received 22 August 2000; received in revised form 20 February 2001; accepted 15 May 2001 1. Introduction The existence of local solutions to the initial value problem x ′ ∈- @V (x)+ F (x); x(0)= x 0 ; (1) where @V is the subdierential of a proper convex lower semicontinuous function and F is an upper semicontinuous, cyclically monotone, compact valued multifunction, was proved by Cellina and Staicu in [5]. Among many improvements of this result, we refer to [8,9]. In [9] an existence result was proved for the Cauchy problem x ′ ∈- @V (x)+ F (x)+ f(t; x); x(0)= x 0 ; (2) where @V and F are as in (1) and f is a Carath eodory function. This problem contains as a special case the problem in (1) and the problem x ′ ∈ F (x)+ f(t; x); x(0)= x 0 ; considered by Ancona and Colombo in [1]. Recently, Papalini obtained in [8] the local existence for the Cauchy problem x ′ ∈- @ F V (x)+ F (x); x(0)= x 0 ; (3) where @ F V is the Fr echet subdierential of a function V with a  -monotone subdier- ential of order 2 and F is an upper semicontinuous, cyclically monotone multifunction. Since the class of proper convex, lower semicontinuous functions is strictly contained  This paper was completed while the rst author was a postdoctoral fellow at the research unit “Mathe- matics and Applications” of the Department of Mathematics of Aveiro University. * Corresponding author. E-mail address: vasile@ua.pt (V. Staicu). 0362-546X/02/$-see front matter c  2002 Elsevier Science Ltd. All rights reserved. PII:S0362-546X(01)00799-4