Energy critical fourth-order Schrödinger equations with subcritical perturbations

In this paper, we study the global well-posedness and scattering theory of an 8-D cubic nonlinear fourth-order Schrödinger equation, which is perturbed by a subcritical nonlinearity. We utilize the strategies in Tao et al. (2007) [16] and Zhang (2006) [17] to obtain when the cubic term is defocusing, the solution is always global no matter what the sign of the subcritical perturbation term is. Moreover, scattering will occur either when the pertubation is defocusing and 1<p<2 or when the mass of the solution is small enough and 1≤p<2.