Well-posedness of a higher-order Schrodinger-Poisson-Slater system

In this paper, we show the global well-posedness of a higher-order nonlinear Schrodinger equation. Specifically, we consider a system of infinitely many coupled higher-order Schrodinger-Poisson-Slater equations with a self-consistent Coulomb potential. We prove the existence and uniqueness global in time of solutions in L-2(R-3) and in the energy space.