A resonance case of the existence of solutions of a quasilinear second-order differential system, which are represented by Fourier series with slowly varying parameters

Abstract

For a quasilinear second-order differential system, whose coefficients have the form of Fourier series with slowly varying coefficients and frequency, we prove, under certain conditions, the existence of a particular solution having a similar structure. This result is obtained in the case where the characteristic equation possesses purely imaginary roots, which satisfy a certain resonance relation.