非齐次超双曲型方程的中量定理的逆定理  

Inverse Theorem of Mean Value Theorem for Nonhomogeneous Ultrahyperbolic Equation

作　　者：容跃堂[1] 孙法国[1] 马福敏 

机构地区：[1]西北纺织工学院基础部

出　　处：《西北纺织工学院学报》1997年第2期172-174,181,共4页Journal of Northwest Institute of Textile Science and Technology

摘　　要：讨论了２ｍ个变元非齐次超双曲型方程的中量性质．利用基本公式及适当的不等式估计，得到了中量定理的逆定理．证明了函数ｕ（ｘ，ｙ）在∑ｍｉ＝１（ｘｉ－ｘｉ０）２＝ｒ２和∑ｍｉ＝１（ｙｉ－ｙｉ０）２＝ｓ２上的中量满足某一恒等式时，ｕ（ｘ，ｙ）是２ｍ个变元非齐次超双曲型方程的解．The property of mean value of solutions for nonhomogeneous ultrahyperbolic equation of 2 m variables is studied. By using fundamental formula and adaptable estimation of inequality, inverse theorem of mean value theorem is given. It is proved that u(x,y) is a solution of nonhomogeneous ultrahyperbolic equation of 2 m variables, if mean value of u(x,y) on ∑ mi=1(x i-x i 0) 2=r 2,∑mi=1(y i-y i 0) 2=s 2 satisfies an identity.

关 键 词：非齐次 超双曲型方程 中量定理 逆定理 

分 类 号：O175.27[理学—数学]