Unbounded connected component of the positive solution set of nonlinear operator equation and its applications

In this paper, by using global bifurcation theories we obtain some results for structure of positive solution set of some nonlinear equations with parameters. As a result, we obtain some existence results for positive solutions of the nonlinear operator equation. The main result can be applied to various of differential boundary value problems to obtain the existence results for positive solutions without the assumption that the nonlinearities are positone.