THE INITIAL BOUNDARY VALUE PROBLEM FOR QUASI-LINEAR SCHRÖDINGER-POISSON EQUATIONS

In this article, the author studies the initial-(Dirichlet) boundary problem for a high-field version of the Schrödinger-Poisson equations, which include a nonlinear term in the Poisson equation corresponding to a field-dependent dielectric constant and an effective potential in the Schrödinger equations on the unit cube. A global existence and uniqueness is established for a solution to this problem.