Abstract
We examine a one-dimensional steady-state diffusion model for a biological population in which individuals collected either throughout the domain or from one endpoint of the domain are returned to the population at a discrete set of locations. Specifically, the modeling equations are u″(x)+f(x,u(x))+(∑ni=1κiδβi(x))g(∫10α(s)u(s)ds)=0 in the former case and u″(x)+f(x,u(x))+(∑ni=1κiδβi(x))g(u′(0)) in the latter case, where the function g specifies the rate of return and f is the usual net population growth term. With Dirichlet boundary conditions imposed at both ends of the domain, the topological transversality theorem is used to show that a positive solution exists provided g does not increase too rapidly.
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