Existence results for a superlinear singular equation of Caffarelli-Kohn-Nirenberg type

In this paper, using Mountain Pass Lemma and Linking Argument, we prove the existence of nontrivial weak solutions for the Dirichlet problem for the superlinear equation of Caffarelli-Kohn-Nirenberg type in the case where the parameter $\lambda \in (0,{\lambda }_2)$, ${\lambda }_2$ is the second positive eigenvalue of the quasilinear elliptic equation of Caffarelli-Kohn-Nirenberg type.