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Open Access Research

Dirichlet problem for the Schrödinger operator on a cone

Lei Qiao1* and Guan-Tie Deng2

Author Affiliations

1 Department of Mathematics and Information Science, Henan University of Economics and Law, Zhengzhou, 450002, P.R. China

2 School of Mathematical Science, Laboratory of Mathematics and Complex Systems, MOE Beijing Normal University, Beijing, 100875, P.R. China

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Boundary Value Problems 2012, 2012:59  doi:10.1186/1687-2770-2012-59

Published: 18 June 2012

Abstract

In this article, a solution of the Dirichlet problem for the Schrödinger operator on a cone is constructed by the generalized Poisson integral with a slowly growing continuous boundary function. 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.

MSC: 31B05, 31B10.

Keywords:
Dirichlet problem; stationary Schrödinger equation; cone