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Volume 6,     Number 3,     Fall 1998

 

A BRIDGE BETWEEN THE
BENDIXSON-DULAC CRITERION IN R2
AND LIAPUNOV FUNCTIONS IN Rn
J.A. PACE AND M.L. ZEEMAN

Abstract. In this paper we generalize a theorem of Busenberg and van den Driessche from three dimensions to arbitrary finite dimension, thereby giving a new criterion for ruling out certain oriented periodic orbits from autonomous differential equations in Rn. As in the three-dimensional case, this theorem can be viewed as generalizing both the classical Bendixson-Dulac criterion and the theory of Liapunov functions.

 

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