Vortex Solutions Of The Nonlinear Schrodinger Equation

In this paper,we consider the existence of vortex solutions to the following three types of equation.First:field equation(?)(0.0.4)Second:Choquard type of equation(?)(0.0.5)Third:Schrodinger-Poisson type of equation(?)(0.0.6)(V):k>2,N?4,p(x)is a continuous nonnegative function on RN satisfying#12?k??<?k+1,?k is the eigenvalue of the operator-?+p(x),?>0.We prove the existence of solutions in each case for 0<?<?i,i=1,2,3 with some ?i>0,i=1,2,3.The thesis consists of four chapters.In the first chapter,we introduce the background of the problem,main results of the paper and preliminary knowledge.In the second chapter,we obtain the vortex solution of field equation(0.0.4)by using Linking theorem.In the third chapter,using the Linking theorem,we get the vortex solution of Choquard type of equation(0.0.5).In the fourth chapter,we use truncation method to obtain the vortex solution of Schrodinger-Poisson type of equation(0.0.6).