Authors: L.Cesari and Heinz W. Engl
Abstract: In this paper we use the Leray-Schauder degree to prove various existence results for nonlinear alternative problems in a Banach space, which generalize a Hilbert space result due to Cesari, Kannan and McKenna. Using a result due to Kellog, we also prove a uniqueness theorem. We apply the abstract result to the problem of existence of a periodic solution for a nonlinear differential equation.