In this paper, using the Mountain Pass Lemma and the LinkingArgument, we prove the existence of nontrivial weak solutions forthe Dirichlet problem for the superlinear equation of Caffarelli-Kohn- Nirenberg type in the case where the parameter L  in (0, L2), L2 being the second positive eigenvalue of the quasilinear elliptic equation of Caffarelli-Kohn-Nirenberg type.