Multiple global bifurcation branches for nonlinear Picard problems

In this paper we prove the global bifurcation theorem for the nonlinear Picard problem. The right-hand side function ' is a Caratheodory map, not differentiable at zero, but behaving in the neighbourhood of zero as specified in details below. We prove that in some interval [a,b] R the Leray-Schauder degree changes, hence there exists the global bifurcation branch. Later, by means of some approximation techniques, we prove that there exist at least two such branches.