两个函数方程与双曲方程组特征问题——有不唯一解的充要条件

TWO FUNCTIONAL EQUATIDNS AND GOURSAT'S PROBLEMS OF HYPERBOLIC——NECESSARY AND SUFFICIENT CONDITIONS IN NONUNIQUE SOLUTIONS

本文继续前两文[2—3]的工作,首先讨论两个函数方程有不唯一解的充分必要条件,并应用这结果研究双曲方程组(H_1)两种定解条件的特征问题有不唯一解的充分必要条件,找出所有不唯一解。

In this paper we discuss the necessary and sufficient conditions for the existing non-unique solutions for two functional equations. With these results, we oltain the necessary and sufficient conditions for the existing noln-unique solutions and thier non-unique solu lions for a class of Goursat's probems of the hyperbolic system of the second order (H_1).