@MISC{Ramm_onthe, author = {A. G. Ramm}, title = {On the DSM Newton-type method}, year = {} }

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Abstract

A wide class of the operator equations F (u) = h in a Hilbert space is studied. Convergence of a Dynamical Systems Method (DSM), based on the continuous analog of the Newton method, is proved without any smoothness assumptions on the F ′ (u). It is assumed that F ′ (u) depends on u continuously. Existence and uniqueness of the solution to evolution equation ˙u(t) = −[F ′ (u(t))] −1 (F (u(t)) − h), u(0) = u0, is proved without assuming that F ′ (u) satisfies the Lipschitz condition. The method of the inverse function theorem.