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Integral representation for the solution of the stationary Schrodinger equation in a cone

Abstract: In this paper, we consider the Dirichlet problem for the stationary Schrodinger equation in a cone with continuous boundary data. For a solution u of the stationary Schrodinger 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.