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Integral representation for the solution of the stationary Schrödinger equation in a cone
Author(s) -
Qiao Lei,
Deng Guantie
Publication year - 2012
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201100251
Subject(s) - mathematics , cone (formal languages) , dirichlet boundary condition , mathematical analysis , integral equation , boundary (topology) , boundary value problem , schrödinger equation , representation (politics) , dirichlet distribution , light cone , mathematical physics , algorithm , politics , political science , law
In this paper, we consider the Dirichlet problem for the stationary Schrödinger equation in a cone with continuous boundary data. For a solution u of the stationary Schrödinger equation in a cone, we prove that if its positive part u + satisfying a slowly growing condition, then its negative part u − can also be dominated by a similar slowly growing condition. Meanwhile, u can be represented by its integral in the boundary of the cone.