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Systems of differential inequalities with initial time difference. (English) Zbl 1077.39024

Ukr. Mat. Zh. 56, No. 1, 139-145 (2004) and Ukr. Math. J. 56, No. 1, 173-182 (2004).
The author finds conditions under which the inequalities \[ \alpha'(t)\leq F(t,\alpha (t)),\quad t\geq t_0\geq 0,\alpha (t_0)\leq x_0; \]
\[ \beta'(t)\leq F(t,\beta (t)),\quad t\geq \tau_0\geq 0,\beta (\tau_0)\geq x_0 \] (or more general ones) imply an inequality of the form \(\alpha (t)\leq \beta (\Delta (t))\) for \(t\geq t_0\), and \(\alpha (\Delta^{-1}(t))\leq \beta (t)\) for \(t\geq \tau_0\).

MSC:

39B62 Functional inequalities, including subadditivity, convexity, etc.
26D10 Inequalities involving derivatives and differential and integral operators
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