一类半线性椭圆型方程正解的唯一性

Uniquness of Positive Solution of Semilinear Elliptic Equations

摘要: 利用变分原理将问题△ｕ＋ｕｐ＋ｕｑ＝０，ｕ＞０，ｘ∈ＢＲ，ｕ｜ＢＲ＝０正解唯一性的讨论变成一个有约束条件的极值问题，用约束问题解的性质，证明原问题正解的唯一性。

Abstract: Using variational principle,the problem △u+u p+u q=0,x∈B R,u0,x∈B R,u| B k =0 is treated as minimizers of a suitable contrained minimization problem,and some information about minimizers is obtained. Then the uniqueness result is given.