A note on the theorem on differential inequalities. (English) Zbl 1009.34057

Bravyi, E.; Lomtatidze, A.; Půža, B.

Georgian Math. J. 7, No. 4, 627-631 (2000).

The authors consider the Cauchy problem \[ u''(t) = l(u)(t)+q(t), \quad u(a)=c, \] where \(l \) is a linear nonpositive operator. The aim of this note is to derive a necessary condition on \(l \) to be a Volterra operator.

Reviewer: E.V.Shchetinina (Berlin)

MSC:

34K06	Linear functional-differential equations
34K12	Growth, boundedness, comparison of solutions to functional-differential equations

Keywords:

Cauchy problem; linear nonpositive operator