Infinitely Many Sign Changing Solutions For The Nonlinear Schr(?)dinger Equations In R~N

In this paper,we study the multiplicity solutions for some nonlinear Schrodinger e-quations.Depending on Finite-Dimensional Reduction,we use the number of the bumps of the solutions as the parameter to construct the sign-changing solutions for the nonlin-ear Schrodinger equation.We consider the following nonlinear Schrodinger equation-?u + V(x)u=|u|p-1u,u?H1(RN).(0.2)where V(x)is a positive and radial function;1<p<N+2/N-2 if N ? 3;1<p<+?if N = 2.We show that if V(r)has the following expansion:there are constants a>0,m>0,0>0,V0>0,such that V(r)?V0-a/rm+O(1/rm+?),as r?+?then(0.2)has infinitely many non-radial sign-changing solutions,where energy can be made arbitrarily large.