Uniqueness of the Positive Radial Solution on an Annulus

时间:2022-05-25 14:06:55
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文件名称:Uniqueness of the Positive Radial Solution on an Annulus

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更新时间:2022-05-25 14:06:55

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The purpose of this note is to prove uniqueness of the positive radial solution to the Dirichlet problem for 2u& u+ u3=0, (1.1) on the annulus 0= [x # R3 : R1 <| x|< R2] where 0< R1 < R2 ; (the Dirichlet condition at R 2= is interpreted, as usual, to mean that the solution belongs to L2(0)). In [2], uniqueness on a ball and uniqueness to within translation on R3 were proved for the positive radial solution of the Dirichlet problem for this equation.


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