Existence for a diffusing population with returns from the boundary to the interior

Abstract

Conditions sufficient for existence of nonnegative or positive solutions are established for a model of population growth in which individuals reaching the boundary are returned to the interior. The model is a boundary value problem for a nonlocal ordinary differential equation in which occur terms involving the derivative of the solution evaluated on the boundary of the domain.

Keywords:

• Existence
• population control
• nonlocal ordinary differential equations