Global Existence Results for Linear Analytic Partial Differential Equations

By means of a continuity method some global existence theorems are proved, relating the existence domains of the solutions of non-characteristic Cauchy problems to the growth of the leading coefficients of the equation. This is done in n + 1 and n + 1 as corollaries existence results due to Persson and Miyake are obtained. Also, some results by dal Fabbro, Furioli Martinolli, and Ricci, as well as by Jannelli and Kajitani, are extended. Corresponding theorems are proved for real analytic hyperbolic equations.