In this note, we consider a differential-operator equation in a Hilbert space $H$ connected with oscillations of stratified fluids. In terms of the distribution of the spectrum of an operator A we investigate the stability of solutions. In the case where $H = L_2[a,b]$ and $A$ is some selfadjoint extension of the minimal operator generated by the expression $-d^2$/$dx^2,$ this equation is the equation of the dynamics of a stratified fluid. We have obtained necessary and sufficient conditions for the stability of solutions of boundary value problems for this equation.

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