The Classification Of Solutions To Weighted Lane-Emden Equations And Systems

In this thesis,we study the Liouville type theorem about the stable solution and finite Morse index solutions of(?)in unbounded domain and the symmetry of the solution of the system(?)For the Lane-Emden equation with some degenerate items,we use some analysis techniques to get the energy estimate of the stable solution,and finally we have the Liouville-type theorem in some suitable case.It compensates for the Liouville-type the-orem of the Lane-Emden equation when the degenerate term depends only on x.For Hartree type Lane-Emden equations with non-local terms,this paper mainly uses the moving plane method of integral form and Hardy-Littlewood-Sobolev inequality to obtain the symmetry of the solutions of the equations.