Well-posedness of a higher-order Schrödinger–Poisson–Slater system

Abstract

Abstract In this paper, we show the global well-posedness of a higher-order nonlinear Schrödinger equation. Specifically, we consider a system of infinitely many coupled higher-order Schrödinger–Poisson–Slater equations with a self-consistent Coulomb potential. We prove the existence and uniqueness global in time of solutions in L2(R3) $L^{2}( \mathbb{R}^{3})$ and in the energy space.

Keywords

• Nonlinear Schrödinger equations
• Nonlinear Schrödinger–Poisson equations