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 <!-- MATH $u + TNu = f$ --> is given. Here N denotes a (nonlinear) monotone mapping of a real reflexive Banach space X into its conjugate space <!-- MATH ${X^ \ast }$ --> and T a bounded monotone linear operator of <!-- MATH ${X^ \ast }$ --> into X. It is not assumed that T or N is coercive.