## Existence and Uniqueness Theorems for a Class of Linear Fuchsian Partial Differential Equations

J. Math. Sci. Univ. Tokyo
Vol. 6 (1999), No. 3, Page 527--538.

Lope, Jose Ernie C.
Existence and Uniqueness Theorems for a Class of Linear Fuchsian Partial Differential Equations
We will consider linear Fuchsian partial differential operators of the form $\PP = (tD_t)^m + \sum_{j=0}^{m-1}\sum_{|Î±|\leq m-j} a_{j,Î±}(t,z)\cdot (Î¼(t)D_z)^Î± (tD_t)^j .$ For this class of operators, we will formulate existence and uniqueness theorems which are slightly more general than the ones obtained by Baouendi and Goulaouic in 1973. We will specify some properties of the function $Î¼(t)$ and assert that a property is necessary for our theorems to hold.