Critical and Subcritical Fractional Hamiltonian Systems of Schrödinger Equations with Vanishing Potentials

We analyze a class of fractional Hamiltonian systems of Schrödinger equations in RN involving vanishing potential with critical and subcritical nonlinearity. We make use of variational methods to prove the existence of at least one pair of positive solutions. Our result in the critical case is new even for the Laplacian operator. © 2022 Elsevier Ltd