Štěpánková, H. A note on the theorem on differential inequalities. (English) Zbl 1072.34072 Electron. J. Qual. Theory Differ. Equ. 2005, Paper No. 7, 8 p. (2005). Summary: It is proved that if a linear operator \(\ell:C([a,b];\mathbb R)\rightarrow L([a,b];\mathbb R)\) is nonpositive and for the initial value problem \[ u''(t)=\ell(u)(t)+q(t),\quad u(a)=c_1,\quad u'(a)=c_2, \] the theorem on differential inequalities is valid, then \(\ell\) is an \(a\)-Volterra operator. Cited in 1 Document MSC: 34K12 Growth, boundedness, comparison of solutions to functional-differential equations 34K06 Linear functional-differential equations Keywords:differential inequalities; Volterra operator PDFBibTeX XMLCite \textit{H. Štěpánková}, Electron. J. Qual. Theory Differ. Equ. 2005, Paper No. 7, 8 p. (2005; Zbl 1072.34072) Full Text: EMIS