Radial And Non-radial Solutions For A Nonlinear Schrodinger Equation With A Constraint

In this paper,we consider the existence of solutions for a class of semilinear schrodinger equation in L2-subcritical case.The equation is as follows:(?)for 2<p<2+4/N.This paper is mainly divided into two parts.In the first part,we obtain the existence of radial and non-radial solutions of equation(0.0.1)when potential function Q satisfies the corresponding conditions through constraint minimization method.In the second part,the existence of multiple non-radial solutions of equation(0.0.1)will be explained by Lions’ concentrative compactness method.In this paper,two dimensional subcritical problems are considered first,then four dimensional and subcritical problems above them are considered,and the three dimensional problem is left to be solved.