International Journal of Mathematics and Mathematical Sciences
Volume 32 (2002), Issue 2, Pages 73-80

The generalized Turner-Bradley-Kirk-Pruitt equation

Ray Redheffer

Department of Mathematics, UCLA, Los Angeles 90095-1555, CA, USA

Received 26 October 2001

Copyright © 2002 Ray Redheffer. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Several recent results pertaining to nonlinear equations of ecology are applied to a generalization of the Turner-Bradley-Kirk-Pruitt (TBKP) equation, which illustrates a variety of interesting possibilities as regards persistence and extinction. The chief novelty consists in exploiting the value set of the equation, that is, the set of values taken on by the solution as t increases from 0 to . This aspect of the subject depends on a new formulation of a condition that was first introduced by Vance and Coddington in 1989.