Relying on the Yosida approximate, we investigate the problem of finding zeroes for a difference of two maximal monotone operators in Hilbert spaces. These zeroes are compared to those of the corresponding regularized and dual problems. The behavior of the regularized operator is also studied and a splitting algorithm involving the resolvents of both operators is suggested via a fixed-point formulation of the regularized problem. A particular attention is given to the DC programming case.