Infinitely Many Solutions For The Complex Valued Schr(?)dinger Equation With Slow Decaying Of Potential

In this paper,we study the multiplicity solutions for a class of nonlinear Schr(?)dinger equations in electromagnetic field under the condition of slow decaying of potential.Depending on finite dimensional reduction,we use the number of the bumps of the solutions as the parameter to construct the complex valued solutions for the equation.We consider the following equation(?/i-A(y))~2u+V(y)u=f(y)|u|^p-1u.where 1N?C,A:R^N?R^Nis a smooth function,V:R^N?R is a continuous function,f:R^N?R is a continuous function.A(y)satisfies the conditions(A1)and(A2),V(y)and f(y)are radially symmetric.A(y),V(y)and f(y)are all bounded.We show that the equation has infinitely many non-radial complex valued solu-tions whose energy can be made arbitrarily large,when A(y),V(y)and f(y)satisfy the conditions(H1),(H2),and(H3)respectively at infinity(see chapter 1 of the paper).This result generalizes the conclusion in[17].