Dirichlet problem for the Schrödinger operator on a cone

Boundary value problems

Lei Qiao¹  Guan-Tie Deng² 

[1] Department of Mathematics and Information Science, Henan University of Economics and Law, Zhengzhou, P.R. China;School of Mathematical Science, Laboratory of Mathematics and Complex Systems, MOE Beijing Normal University, Beijing, P.R. China

关键词: Dirichlet problem;    stationary Schrödinger equation;    cone;   

DOI  :  10.1186/1687-2770-2012-59

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

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.

【 授权许可】

CC BY