Nguyen Thanh Chung - Department of Mathematics, Quang Binh University, ۳۱۲ Ly Thuong Kiet, Dong Hoi, Quang Binh, Viet Nam.

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

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