By means of a continuity method some global existence theorems are pro
ved, relating the existence domains of the solutions of non-characteri
stic Cauchy problems to the growth of the leading coefficients of the
equation. This is done in C(n+1) and R(n+1) as corollaries existence r
esults due to Persson and Miyake are obtained. Also, some results by d
al Fabbro, Furioli Martinolli, and Ricci, as well as by Jannelli and K
ajitani, are extended. Corresponding theorems are proved for real anal
ytic hyperbolic equations. (C) 1995 Academic Press, Inc.