The aim of this note is to study convergence and convergence rates of the regularized solutions for the operator equation of Hammerstein type x + F2F1(x) = f in reflexive Banach spaces under the non-monotone perturbations F h 2 and F h 1 of the operators F2 and F1, respectively.

The aim of this paper is to present an existence theorem for the operator equation of Hammerstein type x + KF (x) = 0 with the discontinuous semimonotone operator F . Then the result is used to prove the existence of solution of the equations of Urysohn type. Some examples in the theory of nonlinear equations in Lp(Ω) are given for illustration.

We analyze collocation methods for nonlinear homogeneous Volterra-Hammerstein integral equations with non-Lipschitz nonlinearity. We present different kinds of existence and uniqueness of nontrivial collocation solutions and we give conditions for such existence and uniqueness in some cases. Finally we illustrate these methods with an example of a collocation problem, and we give some examples ...