一类高维重特征方程Goursat的问题中的离散现象

Discrete Phenomena in the Goursat Problem for Equations with Double Characteristics in High Dimensions

§1 引言人们对具体实的重特征方程的了解还很不充分。,B,B首先举例指出重特征方程在解的光滑性问题中有所谓离散现象,即方程中的参数取一些离散的值时,解突然失去了光滑性。之后,Treves,F又给出一个例子,发现这种离散也出现在Cauchy问题解的唯一性问题中。王光寅等,陆柱家又进一步研究了较Treves,F.例子广泛的一类方程,指出Cauchy问题和Goursat问题的存在性中都有所谓离散现象。

In this paper, the discrete phenomena in the existence and uniqueness or the ana- lytical solution for the Goursat problem are discussed and the main results are obtained as following: 1) If p≠n+2m(m≥0, integer), then (G) has an unique solution; 2) If p=n+2m(m≥0, integer), then (G) has a solution iff φ(x) satisfies certain consis- tency conditions, and the solution is unique iff q≠0.