\documentclass[reqno]{amsart} \AtBeginDocument{{\noindent\small {\em Electronic Journal of Differential Equations}, Vol. 2003(2003), No. 103, pp. 1--8.\newline ISSN: 1072-6691. URL: http://ejde.math.txstate.edu or http://ejde.math.unt.edu \newline ftp ejde.math.txstate.edu (login: ftp)} \thanks{\copyright 2003 Texas State University-San Marcos.} \vspace{9mm}} \begin{document} \title[\hfilneg EJDE--2003/103\hfil A classical solution weakened on the axis] {A classical solution weakened on the axis for a mixed problem of inhomogeneous hyperbolic equations} \author[Raid Al-Momani \hfil EJDE--2003/103\hfilneg]{Raid Al-Momani} \address{Raid Al-Momani \hfill\break Department of Mathematics, Yarmouk University, Irbid, Jordan} \email{raid@yu.edu.jo} \date{} \thanks{Submitted December 20, 2002. Published October 9, 2003.} \subjclass[2000]{35L70, 58J45} \keywords{Weakened classical solutions, hyperbolic equations} \begin{abstract} The main purpose of this paper is to present sufficient conditions, on the forcing term of a mixed problem for three dimensional hyperbolic equations of any even order, for the existence of axially weakened classical solutions. \end{abstract} \maketitle \numberwithin{equation}{section} \newtheorem{theorem}{Theorem}[section] \section{introduction} Let $r=\sqrt{x_1^2+x_2^2+x_3^2}$ and \$G=\{x\in \mathbb{R}^3: 0