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Abstract
It is proved that if a linear operator l : C([a, b], R) → L ([a, b], R) is nonpositive and for the Cauchy problem u″(t) + l(u)(t) + q(t), u(a) = c the theorem on differential inequalities is valid, then l is a Volterra operator.
Key words and phrases:: Linear functional differential equation; theorem on differential inequalities; Volterra operator
Received: 2000-05-29
Published Online: 2010-02-23
Published in Print: 2000-December
© Heldermann Verlag