Existence of solutions for a class of critical Kirchhoff type problems involving Caffarelli-Kohn-Nirenberg inequalities

In this paper, we study the existence of a nontrival weak solution for a class of Kirchhoff type problems with singular potentials and critical exponents. The proofs are essentially based on an appropriated truncated argument, Caffarelli-Kohn-Nirenberg inequalities, combined with a variant of the concentration compactness principle. We also get a priori estimates of the obtained solution

Keywords:

Kirchhoff type problems , Caffarelli-Kohn-Nirenberg inequalities , Critical exponents , Mountain pass theorem