An Ecological Model with Grazing and Constant Yield Harvesting

作者：Causey Ryan^*; Sasi Sarath; Shivaji R

来源：Bulletin of the Belgian Mathematical Society Simon Stevin, 2010, 17(5): 833-839.

We study positive solutions to the steady state reaction diffusion equation with Dirichlet boundary condition of the form:
-Delta u = au - bu(2) - c u(p)/1 + u(p) - K, x is an element of Omega
u = 0, x is an element of partial derivative Omega.
Here Delta u = div(del u) is the Laplacian of u, a, b, c, p, K are positive constants with p >= 2 and Omega is a smooth bounded region with partial derivative Omega an in C(2). This model describes the steady states of a logistic growth model with grazing and constant yield harvesting. It also describes the dynamics of the fish population with natural predation and constant yield harvesting. We study the existence of positive solutions to this model. We prove our results by the method of sub-super solutions.

• 出版日期2010