Existence Of Solutions For Nonhomogeneous Elliptic Equation With Critical Hardy-Sobolev Exponent And Multi-singular Terms

In this paper, we study a nonhomogeneous elliptic equation, which involves the critical Hardy-Sobolev exponents and multi-singular terms. The nonhomogeneous elliptic equation Firstly, for researched problems and background of some description, we gives the corresponding prior knowledge and definitions.Secondly, by employing Ekieland variational principle and Hardy-Sobolev inequality, the existence of one solution at least under some certain conditions is established.Next, this paper proves that the equation has a local minimum solution. By useing the concentration-compactness principle, the existence of a minimizing sequence is established. There is another solution of the equation to exists in a given condition.Lastly, by the achieving functions of the best Hardy- Sobolev constant and some estimation, this paper proves that the given condition is established as the equation has solutions.