A Class Of Nonlinear Fractional Schrodinger Equations

In this paper, we consider the existence and stability of standing waves of the following nonlinear fractional Schrodinger equations with the Hartree type and power type nonlinearities: where a€(0,1), p>2, i2=-1, i2=-1,*denotes the convolution, and ψ(x,t) is a complex-valued function on R3×R,(-Δ)α is the a-fractional Laplacian defined as where the Fourier transform is given byBy using the critical point theory and variational methods combining with some analytic techniques, we show that the equation (2) has a standing wave, moreover this standing wave is orbitally stable.