Existence Of Nontrivial Solutions Of Semilinear Elliptic Equations With Coulomb Potentials On R~3

In this paper,we study a class of semilinear elliptic equations with Coulomb potentials-?u-Z/|x|u=|u|p-2u-?u,u?H1(R3),where 2<p<10/3,? and Z>0 are real parameters.This kind of problem has a strong physical background.Due to the unboundedness of the region,the compactness of Sobolev embedding has been eliminated.In this paper,we focus on the concentration-compactness principle to restore the compactness of minimized sequences.We prove that the above equations have nontrivial solutions,and extend the positive radial solutions in[1]to a general solution.