Infinitely many solutions for a class of nonlinear fractional Schrödinger equations

In this paper, we consider the problem $ \left (-\Delta \right )^{s}u +a\left ( x \right )u = \left |u\right |^{q-2}u $ in $ \mathbb{R}^{N}, $ where $ 0<s<1, $ $ 2<q<2_{s}^{*} = \frac{2N}{N-2s}, $ $ \left (-\Delta \right )^{s} $ is the fractional Laplacian operator, and the potential function $ a $ is positive, finite and verifies suitable decay assumptions. We obtain the existence of infinitely many solutions by the variational method and the truncation technique.