A counterexample in the theory of linear singularly perturbed systems

In this note we compare the bounded solutions of the linear singularly perturbed system ε X' = A (t) x + f (t), with the solutions of the algebraic system A (t) x + f (t) = 0. Here A and f are bounded C1 functions with bounded derivatives. We assume that the eigenvalues of A (t) satisfy | R...