Abstract
Criteria are established for the correctness of the Cauchy problem for the equationsy (2n)+Ay (n)++By=0,t ε [0, ∞), wheren > 1;A andB are arbitrary commuting self-adjoint operators in a Hilbert space. Forn=2, the criterion is illustrated by the example of the equation describing the dynamics of an exponentially stratified rotating compressible fluid.
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 5, pp. 704–714, May, 1993.
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Shklyar, A.Y. Correctness of the Cauchy problem for trinomial higher-order operator differential equations. Ukr Math J 45, 773–785 (1993). https://doi.org/10.1007/BF01058212
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DOI: https://doi.org/10.1007/BF01058212