Cauchy problem for hyperbolic operators with triple effective characteristics on the initial plane

Abstract

We study the Cauchy problem for effectively hyperbolic operators $P$ with triple characteristics points lying on the initial plane $t= 0$. Under some conditions on the principal symbol of $P$ one proves that the Cauchy problem for $P$ in $[0, T] \times \Omega \subset {\mathbb R}^{n+1}$ is well posed for every choice of lower order terms. Our results improves those in [11] since we do not assume the condition (E) of [11] to be satisfied.