On the investigation of oscillations of quasilinear systems with almost-periodic coefficients : PMM vol.43, no. 6, 1979, pp. 980–991

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.