Weighted fractional Laplace equation involving singular and critical nonlinearity

In this paper, we study the existence of positive solutions of the weighted fractional Laplace problem involving a singular term and a weighted critical Sobolev exponent. By using the idea of Nehari manifold methods and fibering maps, together with variational methods and the fractional Caffarelli-Kohn-Nirenberg inequality, we will prove that there exists at least two positive solutions when we have an appropriate choice of λ.