On the existence of partially irregular almost periodic solutions of linear nonhomogeneous differential systems in a critical nonresonance case (Q2387931)

This paper concerns the linear nonhomogeneous differential system \[ x'(t)= A(t) x(t)+ \varphi(t),\quad (t,x)\in\mathbb{R}\times \mathbb{R}^n, \] where \(A(t)\) is an \(n\times n\)-matrix function and \(\varphi(t)\) is an \(n\)-vector function, both almost-periodic. The existence of irregular almost-periodic solutions in a particular nonresonance case is investigated.