Abstract:

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

Key words: Quasi-linear Schrodinger-Poisson system, Dirichlet boundary conditions,
global existence and uniqueness