Multiple Solutions of Nonlinear Schrodinger Equation with the Fractional p-Laplacian

We use two variant fountain theorems to prove the existence of infinitely many weak solutions for the following fractional p-Laplace equation (-Delta)(p)(alpha)u + V (x)vertical bar u vertical bar(p-2)u = f (x, u), x is an element of R-N, where N >= 2, p >= 2, alpha is an element of (0,1), (-Delta)(p)(alpha) is the fractional p-Laplacian and f is either asymptotically linear or subcritical p-superlinear growth. Under appropriate assumptions on V and f, we prove the existence of infinitely many nontrivial high or small energy solutions. Our results generalize and extend some existing results.