  The paper is devoted to investigating a Cauchy problem for nonlinear elliptic
PDEs in the abstract Hilbert space. The problem is hardly solved by computation
since it is severely ill-posed in the sense of Hadamard. We shall use a
modified integral equation method to regularize the nonlinear problem with
globally and locally Lipschitz source terms. Convergence estimates are
established under priori assumptions on exact solution. A numerical test is
provided to illustrate that the proposed method is feasible and effective.
These results extend some earlier works on a Cauchy problem for elliptic
equations.
