Joon Hyuk Kang, Lucinda Ford
abstract:
The purpose of this paper is to give sufficient conditions for the existence and
uniqueness of positive solutions to a rather general type of elliptic system of
the Dirichlet problem on a bounded domain $\Omega$ in $R^{n}$. Also considered
are the effects of perturbations on the coexistence state and uniqueness. The
techniques used in this paper are super-sub solutions method, eigenvalues of
operators, maximum principles, spectrum estimates, inverse function theory, and
general elliptic theory. The arguments also rely on some detailed properties for
the solution of logistic equations. These results yield an algebraically
computable criterion for the positive coexistence of species of animals with
predator-prey relation in many biological models.
Mathematics Subject Classification: 35J57, 35J67
Key words and phrases: Predator-prey system, coexistence state, existence, uniqueness, perturbation