The influence of a metasolution on the behaviour of the logistic equation with nonlocal diffusion coefficient

In this paper we use the bifurcation method and fixed point arguments to study a logistic equation with nonlocal diffusion coefficient. We prove the existence of an unbounded continuum of positive solutions that bifurcates from the trivial solution. The global behaviour of this continuum depends strongly on the value of the nonlocal diffusion coefficient at infinity as well as the relative position between the refuge of the species and the weight of the diffusion coefficient. Moreover, we show the complexity of the structure of the set of positive solutions using fixed point arguments.