Abstract

The results by Gording, Larsson, Cattabriga, Rodino, Calvo on correctness of Cauchy problem for N-hyperbolic equations are generalized. We prove that in the general case where the vector N = (N1, …,Nn) is different from the vector (1, 0, …, 0), for the correctness of the Cauchy problem more stronger condition is required, which we call weighted hyperbolicity condition. We also discuss the properties of polynomials possessing weighted hyperbolicity property.

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