Global structure of supercritical bifurcation with turning points for the logistic elliptic equation with nonlinear boundary conditions

In this paper, we give rather complete descriptions of the global bifurcation diagrams of positive solutions for the logistic elliptic equation with nonlinear boundary conditions in three cases of an included weight function. Besides the abstract theory of local and global bifurcation, careful observation of the reduced bifurcation equation in finite dimensional space and blow up arguments for the corresponding initial boundary value problem play an important role in characterizing the global behavior of the bifurcating positive solutions for values of a parameter. The critical case is dealt with by using a topological technique proposed by Whyburn.