International Journal of Mathematics and Mathematical Sciences
Volume 32 (2002), Issue 2, Pages 73-80
doi:10.1155/S016117120211043X
The generalized Turner-Bradley-Kirk-Pruitt equation
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.
Abstract
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.