Estimates for the Green functions of nonautonomous higher order differential equations

Abstract

Abstract. We consider the equationwhere a 0 (t) ≡ 1; a k (t) (k = 1, ..., n) are bounded continuous functions. It is assumed that all the roots r k (t) (k = 1, ..., n) of the polynomial z n + a 1 (t)z n−1 + ... + a n (t) are real for all t ≥ 0. Sharp estimates for the Green function to the Cauchy problem and their derivatives are derived.