We consider an inclusion problem governed by a strongly monotone Lipschitz continuous operator de ned on a real Hilbert space. We list the assumption on the data and recallthe existence of a unique solution to the problem. Then we introduce several Tykhonovtriples, compare them and prove the corresponding well-posedness results. Moreover, us-ing the approximating sequences generated by these triples, we obtain various convergence results. In particular, with a specific choice of the Tykhonov triple, we deduce a criterion of convergence to the solution of the inclusion. The proofs of our results are based on arguments of compactness, pseudomonotonicity, convexity, fixed point and the Moscoconvergence of sets.