Steady state reaction diffusion equations with falling zero reaction terms and nonlinear boundary conditions

Abstract: We study the structure of positive solutions to classes of steady state ecological models, with negative density dependent dispersal on the boundary. We have established new existence, uniqueness, stability, and bifurcation theory results for these ecological models. Next, we study positive solutions for an infinite semipositone model involving a reaction term with a falling zero and nonlinear boundary conditions at one of the boundary point. Again we have established new existence, nonexistence, and uniqueness results for this infinite semipositone model. We have also provided exact bifurcation diagrams for positive solutions when n = 1 and when the equations are autonomous.