Positive solutions of a nonlocal singular elliptic equation by means of a non-standard bifurcation theory

We consider a nonlocal elliptic equation arising in a prey-predator model whose nonlocal term is singular. We use the Leray-Schauder degree to prove the existence of an unbounded continuum of positive solutions emanating from the trivial solution. As application, we study nonlocal and singular elliptic equations of the type logistic and Holling-Tanner.