2017
Том 69
№ 6

All Issues

Some remarks on linear functional differential inequalities of hyperbolic type

Šremr J.

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Abstract

It is proved that for the validity of a theorem on differential inequalities for the hyperbolic equation $$ \frac{\partial^2u(t, x)}{\partial t \partial x} = l(u)(t,x)+q(t,x)$$ with a nonincreasing linear operator $l: {C}([a, b]\times [c,d];\mathbb{R})\rightarrow{L}([a, b]\times [c,d];\mathbb{R})$, it is necessary that the operator indicated be an $(a, c)$-Volterra operator.

English version (Springer): Ukrainian Mathematical Journal 60 (2008), no. 2, pp 327-337.

Citation Example: Šremr J. Some remarks on linear functional differential inequalities of hyperbolic type // Ukr. Mat. Zh. - 2008. - 60, № 2. - pp. 283–292.

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