Abstract
A criterion for the stability on a finite time interval, with respect to a given measure, of parametrically excited distributed processes is obtained. To this end the comparison method is used in conjunction with Lyapunov's second method and extremal properties of the Rayleigh ratios for self-adjoint operators in Hilbert space. Sufficient conditions for technical stability with respect to a given measure are established for the problem of a fixed strut loaded by a longitudinal dynamic force.
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