Uniqueness of bounded weak solutions to the equation \(u'(t)=a(t)Au(t)\) in Hilbert spaces. (English) Zbl 0669.34039

Zaidman, S.

Libertas Math. 8, 65-67 (1988).

The author considers ultraweak solutions on the whole real line of the equation (vectorvalued functions) \(u'(t)=a(t)Au(t),\) under some assumptions for the scalar functions a(t) and the hermitian operator A in the Hilbert space H. It is proved that solutions which are norm-bounded over the real line vanish identically.

Reviewer: Zhang Di

MSC:

34C11

Growth and boundedness of solutions to ordinary differential equations

Keywords:

first order differential equation; ultraweak solutions