Correctness of the Cauchy problem for trinomial higher-order operator differential equations - Shklyar, A. Ya. (Ukrains’kyi Matematychnyi Zhurnal, 1993)
Criteria are established for the correctness of the Cauchy problem for the equations y^(2n) + Ay^(n) + By = 0, t [0, ∞) where n > 1, А, В are arbitrary commuting self-adjoint operators in a Hilbert space. For n = 2, the criterion is illustrated by the example of the equation describing the dynamics of an exponentially stratified rotating compressible fluid.