  In a Hilbert space setting, we study the stability properties of the
regularized continuous Newton method with two potentials, which aims at solving
inclusions governed by structured monotone operators. The Levenberg-Marquardt
regularization term acts in an open loop way. As a byproduct of our study, we
can take the regularization coefficient of bounded variation. These stability
results are directly related to the study of numerical algorithms that combine
forward-backward and Newton's methods.
