Question:
Perturbed Linear System
Consider the perturbed linear system
x' = (A + eB(t))x, x is an element of R^n,
where A is a constant matrix, B is a bounded continuous matrix valued function, and e is a small parameter. Assume that all eigenvalues of A have non-zero real part.
1) Show that the only bounded solution of the system is 0.
2) If A has an eigenvalue with zero real part, then is the above still true?