A stochastic nonlinear Schrödinger problem in variational formulation

Abstract

This paper investigates a Schrodinger problem with power-type nonlinearity and Lipschitz-continuous diffusion term on a bounded one-dimensional domain. Using the Galerkin method and a truncation, results from stochastic partial differential equations can be applied and uniform a priori estimates for the approximations are shown. Based on these boundedness results and the structure of the nonlinearity, it follows the unique existence of the variational solution.