Quasiperiodic solutions of linear nonhomogeneous differential equations (Q1603152)

Consider the linear nonhomogeneous differential equation \(\dot x= A(t)x+ \varphi(t)\), \(x\in\mathbb{R}^n\), where \(A(t)\) is a quasiperiodic \(n\times n\)-matrix with frequency basis \(\nu\) and \(\varphi(t)\) is a quasiperiodic \(n\)-vector with frequency basis \(\mu\). Assume that the system has a nonhomogeneity in the form of a trigonometric polynomial whose frequency basis \(\mu\), together with the frequency matrix \(\nu\), forms a rationally linearly independent set. The author derives conditions for the existence of quasiperiodic solutions with frequency basis \(\mu\) and indicates the form of such solutions.