Integral representation for the solution of the stationary Schrödinger equation in a cone | Zendy

Qiao Lei | Zendy; Deng Guantie | Zendy

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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.

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