Solvability and well-posedness of higher-order abstract Cauchy problems (Q1177973)

Sufficient conditions for the exponential well-posedness of the higher order Cauchy problem for \(x^{(n)}(t)=\sum^{n-1}_{i=0}B_ ix^{(i)}(t)\) in a Banach space are given that extend the results by \textit{F. Neubrander} [Trans. Am. Math. Soc. 295, 257-290 (1986; Zbl 0589.34004)]. For the proofs, the equation is formulated as a first order system, and techniques for vector-valued Laplace transforms due to \textit{W. Arendt} [Isr. J. Math. 59, No. 3, 327-352 (1987; Zbl 0637.44001)] are employed.