Rendiconti dell’Istituto di matematica dell’Università di Trieste: an International Journal of Mathematics
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.
