Brezis posed the problem of uniqueness for solutions in a ball for Brezis- Nirenberg problem. it was solved by many people, The main ingredient is the clever way using the Pohozaev Identity. But in dimension two the non linearity is of exponential type and Pohozaev identity is in effective when the exponent is critical. Here I would like to discuss this case in generality and prove the uniqueness and non degeneracy of positive solutions for large solutions.