Bifurcation results for a non-local elliptic equation with a nonlinear boundary condition

In this paper we study a logistic elliptic equation with a nonlinear boundary condition and a nonlocal term. By employing the local and global bifurcation theories, a priori bounds for elliptic equations, blow-up techniques for parabolic equations and the properties of the principal eigenvalues, we establish some existence results for compact and unbounded connected components of the positive solutions set of the nonlocal problem.