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

中文关键词:  Asgeirsson中量定理  Euler-Poisson-Darboux方程  超双曲型方程.

英文关键词:asgeirsson mean  value theorem  E-P-D equation  ultrhyperbolic equation.

中文摘要:

      本文对于高阶方程(?)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，同时也证明了其逆定理也成立.

英文摘要:

      In this paper, we applied the different method, disgussed the partial differential equation of the fouth order (?) and proved the mean value of this equation′s solution satisfied E-P-D equation and proved coverse conclusion, too.