Nontrivial solutions for a class of critical elliptic equations of Caffarelli-Kohn-Nirenberg type

In this paper, we deal with a class of critical elliptic equations related to Caffarelli-Kohn-Nirenberg inequalities. The novelty is the presence of a critical exponent and singular coefficients which may be sign-changing. Existence and non-existence of nontrivial solutions are established by means of the Mountain Pass Theorem and variational identity.