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Quasuhyperbolic factorized differential-operator equations with variable domains of smooth operator coefficients were considered in [1]. In the case of discontinuous operator coefficients, only hyperbolic second-order differential-operator equations were investigated [2, 3]. In the present paper, we prove the strong well-posedness and the smoothness of strong solutions of quasihyperbolic factorized differential-operator equations with variable domains of discontinuous operator coefficients; i.e., one of the main results for hyperbolic second-order differential-operator equations with discontinuous operators in [4] is generalized to the case of quasihyperbolic even-order differentialoperator equations.

Cauchy problem for quasihyperbolic factorized differential equations with variable domains of discontinuous operators