半线性椭圆方程在环域中径向正解的存在唯一性

The Existence and Uniqueness of Semilinear Elliptic Equation in the Annular Region

讨论了二阶半线性椭圆方程△ｕ＋ｆ（ｕ）＝０在环域中的Ｄｉｒｉｃｈｌｅｔ问题，未对ｆ（ｕ）给出增长（临界）指数α＝ｎ＋２ｎ－２的限制，给出了径向正解的先验估计，以及径向正解的存在唯一性。

The Dirichlet problem of semilinear elliptic equation △u+f(u)=0,x∈Ω;u=0,x∈Ω was discussed,where Ω={x|x∈R n,R 1<|x|<R 2,R 1>0},f(0)=0 .The discussion is different from other discussions given before,without restricting critical exponent α=n+2n-2 of the f(u) .We give prior estimates at first,then existence and uniqueness of positive radial solution of the problem are also given.