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

TL;DR

This paper develops a Dynamical Systems Method for solving ill-posed nonlinear equations involving monotone, locally Hölder continuous operators, introducing a discrepancy principle under weak assumptions with minimal smoothness requirements.

Contribution

It extends the Dynamical Systems Method to handle operators with local Hölder continuity, providing a new discrepancy principle applicable under weak conditions.

Findings

Discrepancy principle justified under minimal smoothness assumptions

Method effective for monotone, locally Hölder continuous operators

Applicable to ill-posed nonlinear equations

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 $\alpha>1/2$.