IJPAM: Volume 85, No. 6 (2013)

POSITIVE EQUILIBRIUM SOLUTIONS TO
GENERAL POPULATION MODEL

Joon Hyuk Kang
Department of Mathematics
Andrews University
Berrien Springs, MI 49104, USA


Abstract. In this paper, we investigate conditions for the existence of positive solution to the following general elliptic system with various growth conditions:

\begin{displaymath}\left\{ \begin{array}{l}
\left.\begin{array}{l}
\Delta u + ...
...ial\Omega} = v\vert _{\partial\Omega} = 0.
\end{array} \right.\end{displaymath}

Our arguments mainly rely on super-sub solutions, maximum principles, spectrum estimates, and some detailed properties for the solution of logistic equations.

Received: March 3, 2013

AMS Subject Classification: 35A05, 35A07

Key Words and Phrases: elliptic system with various growth conditions, existence of positive solution, super-sub solutions, maximum principles, spectrum estimates, logistic equations

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DOI: 10.12732/ijpam.v85i6.4 How to cite this paper?
Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2013
Volume: 85
Issue: 6