The Existence Of Two Weak Solutions Of Critical Elliptic Equations Of Caffarelli-Kohn-Nirenberg Type In R~N

In this paper,we use variational method to study the following critical elliptic equation of Caffaxelli-Kohn-Nirenberg type whereThis kind of problem has strong physics background and research value of mathematics theory.In recent decades,many mathematics workers have done some research on this kind of equation.Combined with previous research methods,we use Local Extremum method and Mountain Pass theorem to prove that the above problem has at least two distinct solutions if is fully small and the relevant parameters satisfy the appropriate conditions.