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2000 Mathematics Subject Classification: 34E20, 35L80, 35L15.
In this paper we study an ODE in the complex plane. This is a key step in the search of new necessary conditions for the well posedness of the Cauchy Problem for hyperbolic operators with double characteristics.
We study a class of third order hyperbolic operators in with triple characteristics on . We consider the case when the fundamental matrix of the principal symbol for has a couple of non vanishing real eigenvalues and is strictly hyperbolic for We prove that is strongly hyperbolic, that is the Cauchy problem for is well posed in for any lower order terms .
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