Ž . JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 213, 1531 1997 ARTICLE NO. AY975327 Continuity of the Upper and Lower Value of Slow Growth Differential Games Franco Rampazzo* Dipartimento di Matematica Pura e Applicata, Uni  ersita di Pado  a, `  ia Belzoni 7, 35131, Pado  a, Italy Submitted by Helene Frankowska ´` Received November 10, 1995 Some continuity properties are proved for a zero sum differential game with an unbounded control and no coercivity assumptions.  1997 Academic Press 1. INTRODUCTION This note concerns the continuity of the upper and lower value for a zero-sum, differential game, with dynamics and payoff of the form x  f t , x , a , c Ž . ˙ xt  x Ž. and T   Pt , x ; a , c  lt , x , a , c dt  g xT , Ž . Ž . Ž . ˙ H t respectively. The goal of the player maneuvering a is to minimize the payoff P, while the player acting by means of c wishes to maximize P. The control a is con  entional, i.e., it takes values in a compact subset A of an Euclidean space  q . On the contrary, the control c is allowed to range over a cone C   m , and it has just to satisfy an integral constraint of the *E-mail address: rampazzo@pdmat1.math.unipd.it. 15 0022-247X97 $25.00 Copyright  1997 by Academic Press All rights of reproduction in any form reserved.