On nonlinear equations of Hammerstein type in Banach spaces

A new theorem on the existence and uniqueness of a solution of an equation of Hammerstein type u + T N u = f u + TNu = f is given. Here N denotes a (nonlinear) monotone mapping of a real reflexive Banach space X into its conjugate space X ∗ {X^ } and T a bounded monotone linear operator of X ∗ {X^ } into X . It is not assumed that T or N is coercive.