On a quasilinear Schrödinger-Poisson system

On a class of nonlinear fractional Schrödinger-Poisson systems

In this paper, we are concerned with the following fractional Schrödinger-Poisson system:    (−∆s)u + V (x)u + φu = m(x)|u|q−2|u|+ f(x,u), x ∈ Ω, (−∆t)φ = u2, x ∈ Ω, u = φ = 0, x ∈ ∂Ω, where s,t ∈ (0,1], 2t + 4s > 3, 1 < q < 2 and Ω is a bounded smooth domain of R3, and f(x,u) is linearly bounded in u at infinity. Under some assumptions on m, V and f we obtain the existence of non-trivial so...

The Schrödinger-Poisson System on the Sphere

Abstract. We study the Schrödinger–Poisson system on the unit sphere S2 of R3, modeling the quantum transport of charged particles confined on a sphere by an external potential. Our first results concern the Cauchy problem for this system. We prove that this problem is regularly well-posed on every Hs(S2) with s > 0, and not uniformly well-posed on L2(S2). The proof of well-posedness relies on ...

Parallel solution of a Schrödinger-Poisson system

We present a parallel solution of the Schrr odinger{Poisson system on distributed memory machines. The Schrr odinger{Poisson system is an evolution model for the numerical simulation of a collisionless electron plasma. We apply the Galerkin{Fourier method to the one{ dimensional system which results in a nonlinear system of ordinary differential equations. This initial value problem is solved b...

About a 1 D Stationary Schrödinger Poisson System

The stationary SchrrdingerrPoisson system with a selffconsistent eeective KohnnSham potential is a system of PDEs for the electrostatic potential and the envelopes of wave functions deening the quantum mechanical carrier densities in a semiconductor nanostructure. We regard both Poisson's and Schrrdinger's equation with mixed boundary conditions and discontinu-ous coeecients. Without an exchang...

Soliton Solutions for Quasilinear Schrödinger Equations