On the generalized semi-relativistic Schrödinger-Poisson system in $\mathbb{R}^n$

W. Abou Salem; Thomas Chen; V. Vougalter

doi:10.4171/dm/400

JournalsdmVol. 18pp. 343–357

On the generalized semi-relativistic Schrödinger-Poisson system in $R^{n}$

W. Abou Salem
Department of Mathematics and Statistics, University of Saskatchewan, Saskatoon S7N 5E6, Canada
Thomas Chen
Department of Mathematics, University of Texas at Austin, Austin, TX, 78712, USA
V. Vougalter
University of Cape Town, Department of Mathematics and Applied Mathematics, Private Bag, Rondebosch 7701, South Africa

$On the generalized semi-relativistic Schrödinger-Poisson system in $\mathbb{R}^n$ cover$

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Abstract

The Cauchy problem for the semi-relativistic Schrödinger-Poisson system of equations is studied in $R^{n}, n \geq 1$ , for a wide class of nonlocal interactions. Furthermore, the asymptotic behavior of the solution as the mass tends to infinity is rigorously discussed, and compared with solutions to the non-relativistic Schrödinger-Poisson system.

Cite this article

W. Abou Salem, Thomas Chen, V. Vougalter, On the generalized semi-relativistic Schrödinger-Poisson system in $R^{n}$ . Doc. Math. 18 (2013), pp. 343–357

DOI 10.4171/DM/400