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

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