Dynamical system method for ill-posed Hammerstein type operator equations with monotone operators

The problem of approximately solving an ill-posed Hammerstein type operator equation KF(x) = y in a Hilbert space is considered, where K is a bounded linear operator and F is a non-linear monotone operator. The method involves the Dynamical System Method (DSM) - both continuous and iterative schemes, studied by Ramm (2005), and known as Tikhonov regularization. By choosing the regularization parameter according to an adaptive scheme considered by Pereverzev and Schock (2005) an order optimal error estimate has been obtained.