A note on the theorem on differential inequalities

H. Stepankova, University of South Bohemia, Ceske Budejovice, Czech Republic

E. J. Qualitative Theory of Diff. Equ., No. 7. (2005), pp. 1-8.

Abstract: It is proved that if a linear operator $\ell:C([a,b];\R)\rightarrow L([a,b];\R)$ 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 {\it differential inequalities} is valid, then $\ell$ is an $a-$Volterra operator.

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