<正>本文讨论方程u_(xx)-x~2u_(tt)+pu_t=0的第二类边值混合问题解的存在性和唯一性中的离散现象。文中证明了当P(?)1,5,9,…时,问题的解是存在且唯一的;而当p=1,5,9,…时,问题的解的存在性遭到了破坏,唯一性也不复成立。或更确切地说,在一定的相容条件下,以及在方程的重特征流形x=0上补充指定适当的数据,新问题的解才是存在和唯一的。

This paper deals with the discrete phenomena in existence and uniqueness in the mixed problem with the second nonhomogeneous boundary condition in the equationuxx-x2utt+put=0. If p≠1, 5, 9, ……, the solution of the problem is not onlyunique but also existing. If p=1, 5, 9, ……, neither uniqueness nor existence canbe found in the solution. In other words, only under some compatible conditions and with some additional data given to the dual characteristic points (when x = 0) in the equation, can the solution of the problem be existing and unigue.