Convergent factorial series solutions of linear difference equations

A generalized Sturmian theorem is proved for elliptic differential inequalities of second order in arbitrary bounded domains G in n-dimensional Euclidean space. Under weaker hypotheses than normally given, no boundary regularity is required for the conclusion that every solution of such an inequality has a zero in G. This is a so-called strong theorem, meaning that the conclusion applies to G rather than $\text{G}\text{?}$. Specialization to linear symmetric elliptic equations sharpens earlier Sturmian theorems.