A heterogeneous diffusive logistic model of a single species population dynamics with predation and harvesting terms

Authors

S S. Rokn e vafa, Sharif University of Technology
H T. Tehrani, University of Nevada, Las VegasFollow

Document Type

Article

Publication Date

1-1-2017

Publication Title

Nonlinear Analysis, Theory, Methods and Applications

Volume

156

First page number:

1

Last page number:

16

Abstract

We study existence and multiplicity of positive solutions of a heterogeneous diffusive logistic equation with predation and harvesting terms, −Δu=au−b(x)u2−c, where a,c,m and d are positive constants, Ω a bounded smooth domain in RN, and b(x) is a nonnegative function on Ω¯, with Ω0 a region such that Ω¯0⊂Ω and Ω¯0={x∈Ω:b(x)=0}. Under the strong growth rate assumption, that is, when a is greater than the first eigenvalue of −Δ in Ω0 with Dirichlet boundary condition, we show that the equation has at least one positive solution for 0≤d0. In addition, in case c

Rokn e vafa, S. S., Tehrani, H. T. (2017). A heterogeneous diffusive logistic model of a single species population dynamics with predation and harvesting terms. Nonlinear Analysis, Theory, Methods and Applications, 156 1-16.
http://dx.doi.org/10.1016/j.na.2017.02.010