Influence of the spatial heterogeneities in the existence of positive solutions logistic BVPs with sublinear mixed boundary conditions

Abstract

In this paper we analyze the influence of the spatial heterogeneities in the existence of positive solutions of Logistic problems with heterogeneous sublinear boundary conditions. We will show that the relative positions of the vanishing sets of the potentials in front of the nonlinearities, in the PDE and on the boundary conditions, play a crucial role as for the amplitude of the range of values of the bifurcation parameter for which the problems possess positive solutions. We will compare the cases of the logistic problem with linear and nonlinear boundary conditions. Also, we will show the global bifurcation diagram of positive solutions of the logistic problem with heterogeneous nonlinear boundary conditions, considering the amplitude of the nonlinearity in the boundary conditions as bifurcation-continuation parameter.