Diffusive logistic equation with non-linear boundary conditions

We analyze the solutions of a population model with diffusion and logistic growth. In particular, we focus our study on a population living in a patch, Ω ⊆ R n with n ⩾ 1 , that satisfies a certain non-linear boundary condition and on its survival when constant yield harvesting is introduced. We establish our existence results by the method of sub-super solutions.