一类Fuchsian型特征算子Cauchy问题非平坦解的唯一性

UNIQUENESS OF NON-FLAT SOLUTION TO THE CAUCHY PROBLEM OF THE FUCHSIAN CHARACTERISTIC OPERATOR

本文考虑见R_z^n×R_t^l上的Fuchsian型特征算子为■在条件(2)～(7)式的假设下,存在正整数h,使P的h阶非平坦解具有唯一性。其结果是文献[2]、[3]、[4]的推广。

Consider the following Fuchsian characteristic operator: P(x,t, tD_t,t^D_t)=(tD_t)~m+a_(a, j) (x,t)(T^D_z)(tD_t). in R_2~n×R_t^l. Under the conditions (1) to (7) as indicated in the text,there exists a positive integer h such that the uniqueness of the non-flat solution to such a Cauchy problem of P of the hth order is guaranteed. Findings in this article are the extension of Refs (1), (2),(3) and (4).