On complete second order linear differential equations in Banach spaces

Ti-Jun Xiao and Liang Jin

Vol. 142 (1990), No. 1, 175–195

DOI: 10.2140/pjm.1990.142.175

Abstract

This paper is concerned with the complete second order equation u′′(t) + Bu′(t) + Au(t) = 0 in a Banach space, where both A and B are densely defined closed linear operators. The main result is a theorem of Hill-Yosida-Phillips type for the Cauchy problem for the equation to be well posed.

Mathematical Subject Classification 2000

Primary: 34G10

Secondary: 47D06

Milestones

Received: 28 December 1987

Revised: 13 March 1989

Published: 1 March 1990