Dynamical Systems Method for solving nonlinear equations with locally Holder continuous monotone operators

Abstract

A version of the Dynamical Systems Method for solving ill-posed nonlinear equations with monotone and locally H\"{o}lder continuous operators is studied in this paper. A discrepancy principle is proposed and justified under natural and weak assumptions. The only smoothness assumption on $F$ is the local H\"{o}lder continuity of order $\alpha>1/2$.