Existence And Radial Symmetry Of Positive Solution Of Fractional Laplacian

In this paper we study existence and radial symmetry of positive solutions of in the whole space Rn, where0<α<2,β>1. Furthermore, we investigate the radial symmetry of positive solutions ofIn chapter one, first, we introduce the research background of the existence, radial symmetry of positive solution of fractional Laplacian and present some basic properties and the motivation. Next, we simply introduce some important theorems and results which we shall use later.In chapter two, firstly, we recall some important definitions and theorems. Secondly, we prove the existence of positive solutions of (0-3) by use the variational approach and mountain pass theorem. Lastly, we prove the radial symmetry of positive solutions of (0-3) by using the moving plane approach.In chapter three, we prove the radial symmetry of positive solutions of (0-4) by using the moving plane approach.