Uniqueness for a nonlinear abstract Cauchy problem

Alan Van Lair

Vol. 144 (1990), No. 1, 105–129

DOI: 10.2140/pjm.1990.144.105

Abstract

Let H be a complex Hilbert space, and let A be a linear, unbounded operator defined on a domain D in H. We show that the Cauchy problem for differential equations and inequalities involving the operator dⁿu∕dtⁿ − Au as the principal part have at most one solution. No symmetry conditions are placed on the operator A.

Mathematical Subject Classification 2000

Primary: 34G20

Secondary: 34A12, 34A40, 47H15

Milestones

Received: 26 April 1988

Revised: 21 February 1989

Published: 1 July 1990