Unilateral Global Bifurcation for Eigenvalue Problems with Homogeneous Operator

We focus on the structure of the solution set for the nonlinear equation u = L (lambda)u + H(lambda, u), where L(.) and H(lambda, u) are continuous operators. Under certain hypotheses on L(.) and H(., .), unilateral global bifurcations for eigenvalue problems are presented. Some applications are illustrated for nonlinear ordinary and partial differential equations. In particular, the existence and multiplicity of one-sign solutions for Monge-Ampere equation is discussed.