关于△u＝f（x，u，gradu）全局解的非存在性

On the Nonexistence of Entire Solution of Differential Equation △u = f(x,u,gradu)

用球平均法证明了方程△ｕ＝ｆ（ｘ，ｕ，ｇｒａｄｕ），当ｆ（ｘ，ｕ，ｇｒａｄｕ）满足一定的条件时，在Ｒｎ上不存在古典的全局解．

The classic nonexistence of entire solution of the differential equation △u = f(x, u,gradu ) in Rn is proved, when f(x,u, gradu ) satisfies some conditions.