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Abstract and Applied Analysis
Volume 2012, Article ID 578197, 14 pages
http://dx.doi.org/10.1155/2012/578197
Research Article

Dirichlet Problem for the Schrödinger Operator in a Half Space

Department of Mathematics and Information Science, Henan University of Economics and Law, Zhengzhou 450002, China

Received 22 April 2012; Accepted 12 July 2012

Academic Editor: Jean Pierre Gossez

Copyright © 2012 Baiyun Su. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

For continuous boundary data, the modified Poisson integral is used to write solutions to the half space Dirichlet problem for the Schrödinger operator. Meanwhile, a solution of the Poisson integral for any continuous boundary function is also given explicitly by the Poisson integral with the generalized Poisson kernel depending on this boundary function.