This dissertation is concerned with the convergences and convergence rates of the solutions from the regularization and perturbation of several classes of nonlinear ill-posed problems in Hilbert spaces.

We consider the convergence of solutions of perturbation for some set-valued nonlinear monotone mappings and obtain a convergence rate for a class of differentiable monotone operators. We also study the Tikhonov regularization in Hilbert scales with linear closed operators for a class of nonlinear operator equations. Finally, we introduce inverse-monotone operators, establish some results on convergence and convergence rate of the solutions of perturbed variational inequalities involving inverse-monotone operators, and generalize the degree of ill-posedness to weakly differentiable operators.