IJPAM: Volume 48, No. 3 (2008)

STEADY STATE PROBLEM OF A COOPERATION MODEL
WITH COMBINED REPRODUCTION AND
SELF-LIMITATION RATES

Joon Hyuk Kang
Department of Mathematics
Andrews University
Berrien Springs, MI 49104-0350, USA
e-mail: kang@andrews.edu


Abstract.The non-existence and existence of the positive solution for the generalized cooperation biological model for two species of animals

\begin{displaymath}\left.\begin{array}{l} \Delta u + u(g_{1}(u) + g_{2}(v)) = 0\... ...\ u = v = 0\;\;\mbox{on}\;\;\partial\Omega, \end{array}\right.\end{displaymath}

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

Received: August 26, 2008

AMS Subject Classification: 62P10

Key Words and Phrases: generalized cooperation biological model, positive solution, elliptic theory, upper-lower solutions, maximum principles and spectrum estimates

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2008
Volume: 48
Issue: 3