Ž . Journal of Mathematical Analysis and Applications 231, 509525 1999 Article ID jmaa.1998.6247, available online at http:www.idealibrary.com on On Third Order Differential Equations with Property A and B Mariella Cecchi Department of Electronic Engineering, Uni  ersity of Florence, Via S. Marta 3, 50139 Firenze, Italy Zuzana Dosla ˇ´ Department of Mathematics, Masaryk Uni  ersity, Janacko  o nam. 2a, 66295 Brno, ´ˇ ´ Czech Republic and Mauro Marini Department of Electronic Engineering, Uni  ersity of Florence, Via S. Marta 3, 50139 Firenze, Italy Submitted by Z. S. Athanasson Received March 4, 1998 INTRODUCTION This paper is concerned with the asymptotic behavior of solutions of the linear differential equations x   qt x '  r t x  0 e  Ž. Ž. Ž . and of the corresponding nonlinear ones x   qt x '  r t f x  0, n  Ž. Ž. Ž . Ž . where q , r are continuous functions for t  0, qt  0, r t  0 H Ž. Ž. Ž . 1 and f is a continuous function in  such that f uu  0 for u  0. H Ž . Ž . 2 509 0022-247X99 $30.00 Copyright  1999 by Academic Press All rights of reproduction in any form reserved.