IJPAM: Volume 53, No. 3 (2009)

NON-NEGATIVE STEADY STATE SOLUTIONS TO
AN ELLIPTIC BIOLOGICAL MODEL

Brian Ibanez$^1$, Joon Hyuk Kang$^2$, Jungho Lee$^3$
$^{1,2}$Department of Mathematics
Andrews University
Berrien Springs, MI 49104, USA
$^1$e-mail: [email protected]
$^2$e-mail: [email protected]
$^3$ABEEK Center
Anyang University
Anyang 5-Dong, Manan-Gu 430-714, Anyang, KOREA
e-mail: [email protected]


Abstract.The non-existence and existence of positive solutions for the generalized predator-prey biological model for two species of animals

\begin{displaymath}\left.\begin{array}{l} \Delta u + ug(u,v) = 0\ \ \mbox{in}\ ... ...u = v = 0\;\;\mbox{on}\;\;\partial\Omega\,, \end{array}\right.\end{displaymath}

is investigated in this paper. The techniques used in this paper are from elliptic theory, the upper-lower solution method, the maximum principles and spectrum estimates. The arguments also rely on detailed properties of solutions to logistic equations.

Received: May 9, 2009

AMS Subject Classification: 78A70, 90B06

Key Words and Phrases: non-existence and existence of positive solutions, generalized predator-prey biological model, logistic equations, maximum principles

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 53
Issue: 3