Abstract
A method is developed for investigating the oscillations of systems with almost-periodic coefficients, based on Kamenkov's ideas [1] on the construction of stationary solutions of systems with periodic coefficients and on the separation of motions. In contrast to [1] it is assumed that under the vanishing of a small parameter μ the system's characteristic equation has, besides n pairs of pure imaginary roots, m zero roots and h roots with negative real parts. Non-resonance and resonance cases are considered. Conditions are obtained for the existence of stationary solutions with respect to terms of first order in the small parameter. An example is presented.
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