On solutions of a second-order quasilinear differential system representable by Fourier series with slowly varying parameters - Kostin, A. V.; Shchegolev, S. A. (Ukrains’kyi Matematychnyi Zhurnal, 1998)
For a second-order quasilinear differential system whose coefficients have the form of Fourier series with slowly varying coefficients and frequency, we prove that, under certain conditions, there exists a particular solution with a similar structure in the case of purely imaginary roots of the characteristic equation for the matrix of coefficients of the linear part.