# zbMATH — the first resource for mathematics

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

##### MSC:
 34K06 Linear functional-differential equations 34K12 Growth, boundedness, comparison of solutions to functional-differential equations
##### Keywords:
Cauchy problem; linear nonpositive operator