Solutions for a class of singular nonlinear boundary value problem involving critical exponent

In this paper, we consider the existence of multiple solutions for a class of singular nonlinear boundary value problem involving critical exponent in Weighted Sobolev Spaces. The existence of two solutions is established by using the Ekeland Variational Principle. Meanwhile, the uniqueness of positive solution for the same problem is also obtained under different assumptions. Supported by the National Natural Science Foundation of China (No. 10631030) and the PhD Sepecialized grant of Ministry of Education of China (No. 20060511001)