We Study the Existence of Radially Symmetric Solitarywaves For a Non-Linear Schrodinger-Poisson System. In Contrast to All Previousresults, We Consider the Presence of a Positive Potential, of Interest Inphysical Applications. We Present a New Implementation of the Two-Grid Methodfor Computing Extremum Eigenpairs of Self-Adjoint Partial Differentialoperators With Periodic Boundary Conditions. a Novel Two-Grid Centereddifference Method Is Proposed For the Numerical Solutions of the Nonlinearschrödinger–Poisson (Sp) Eigenvalue Problem. We Solve the Poisson Equation Toobtain the Nonlinear Potential For the Nonlinear Schrödinger Eigenvalueproblem.