Some remarks on uniqueness for a class of singular abstract cauchy problems


Of concern is the Cauchy problem for equations of the form u (t) + a(t)u'(t) + S2u(t) = 0 ('= d/dt) on a complex Hilbert space X. S is a selfadjoint operator on X while a is a continuous function on (0, ∞) which can be unbounded at t = 0. Uniqueness results are obtained for these equations by applying a uniqueness theorem for nonlinear equations. Furthermore, nonuniqueness examples for the linear abstract Euler-Poisson-Darboux equation, which is contained in this class, show that the uniqueness theorem is best possible. © 1976 American Mathematical Society.

Publication Title

Proceedings of the American Mathematical Society