一类高阶方程的中量定理及其逆定理

The Mean Value Theorem and Converse Theorem of One Class High Order Partial Differential Equations

本文对于高阶方程（_(i=1)∑^(m1)_ (x_i^2)|^( e)_(j=1)∑^(m2)_( y_j^2)|^( e)）~2_u=0在文［２］中量定义的基础上，利用Ａｓｇｅｉｒｓｓｏｎ中量定理，得到了中量所满足的方程，即Ｍ（ｒ，ｓ）＋Ｍ（ｓ，ｒ）满足Ｅ－Ｐ－Ｄ方程，同时也证明了其过定理也成立。

In this paper, we applied the different method, disgussed the partial differential equation of the fouth order (_(i=1)∑^(m1)_ (x_i^2)|^( e)_(j=1)∑^(m2)_( y_j^2)|^( e))~2_u=0 and proved the mean value of this equation's solution satisfied E-P-D equation and proved co- verse conclusion, too.