<正> 1.引言 关于主型偏微分方程的Cauchy问题的唯一性的研究,已经十分充分.事实上,经典的Cauchy-Kovalevsky定理断言,解析方程的非特征Cauchy问题具有唯一性;而Goursat定理则断言,特征Cauchy问题的解必是唯一的,如果特征支柱上只具有单特征的话(参看Hormander[1]第五章).但是,对非主型方程,情形就大不相同.1974年,Treves研

The partial differential equations of non-principal type are far from being wellunderstood. In 1974, F. Treves studied the following Cauchy problem where λ represents a real parameter. By. using the concatenation method, a diserete phenomenon is disclosed. For almost all values of λ, there is uniqueness. However, non-uniqueness occurs only for λ=1, 3, 5,… In this paper, by using energy integral method, we deal with the general second order PDE's of non-principal type in two variables and prove that non-uniqueness is a rare event.