A Trotter–Kato type result for a second order difference inclusion in a Hilbert space

A Trotter–Kato type result is proved for a class of second order difference inclusions in a real Hilbert space. The equation contains a nonhomogeneous term f and is governed by a nonlinear operator A, which is supposed to be maximal monotone and strongly monotone. The associated boundary conditions are also of monotone type. One shows that, if An is a sequence of operators which converges to A in the sense of resolvent and fn converges to f in a weighted l2-space, then under additional hypotheses, the sequence of the solutions of the difference inclusion associated to An and fn is uniformly convergent to the solution of the original problem.