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

We study existence and multiplicity of positive solutions of a heterogeneous diffusive logistic equation with predation and harvesting terms, −Δu=au−b(x)u2−cu1+mu−dh(x)inΩ,∂u∂ν=0on∂Ω, 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