Date of Award

Spring 2-2016

Document Type




First Advisor

Joon Hyuk Kang, Ph.D.


The purpose of this research is to give a sufficient condition for the existence and nonexistence of positive solutions to a rather general type of elliptic system of the Dirichlet problem on a bounded domain. This research was supported by the Office of Research and Creative Scholarship.

The techniques used include upper-lower solutions, eigenvalues of operators, maximum principles, and spectrum estimates. The arguments also rely on some detailed properties of the solutions of logistic equations. These results yields algebraically computable criteria for the positive coexistence of competing species of animals in many biological models.