Application Of The Method Of Moving Plane In Two Kinds Of Nonlinear Elliptic Partial Differential Equations

This paper mainly studies the symmetry of positive solutions of two kinds of nonlinear elliptic partial differential equations:(?).When the coefficient and indexs are in different ranges,the symmetry of solu-tions of the second-order elliptic equations are discussed by using the method of moving plane.The thesis consists of five chapters,which are arranged as follows:In the Chapter one,we present the backgrounds of the problems.In the Chapter two,we introduce some notations and symbols which would be used in this paper,and describe the application of moving plane method briefly.In the Chapter three,we prove the symmetry of solution for-?u=|x|?up+|X|?uq.In Chapter four,we prove the symmetry of solution for-?u=|x|?up+m|x|-2x·?u.In Chapter five,we work into the aspects related to exotic spheres.