  We study Tikhonov regularization for certain classes of non-linear ill-posed
operator equations in Hilbert space. Emphasis is on the case where the solution
smoothness fails to have a finite penalty value, as in the preceding study
'Tikhonov regularization with oversmoothing penalty for non-linear ill-posed
problems in Hilbert scales'. Inverse Problems 34(1), 2018, by the same authors.
Optimal order convergence rates are established for the specific a priori
parameter choice, as used for the corresponding linear equations.
