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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
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