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Oscillations of first-order differential inequalities with deviating arguments. (English) Zbl 0586.34058
Theorems on oscillation of solutions of first-order functional- differential inequalities of the forms $(-1)^ zy'(t)sgn y(t)\geq p(t)\prod^{n}_{i=1}| y(g_ i(t))|^{r_ i}$ and $(- 1)^ zy'(t)sgn y(t)\geq p(t)\sum^{n}_{i=1}p_ i(t)| y(g_ i(t))|,$ where $$z=1,2,r_ i$$ are nonnegative numbers with $$r_ 1+...+r_ n=1$$, $$g_ i:[0,\infty)\to [0,\infty)$$, $$p,p_ i: [0,\infty)\to (0,\infty)$$ are continuous functions and $$\lim_{t\to \infty}g_ i(t)=\infty$$, are proved.
Reviewer: R.R.Akhmerov

##### MSC:
 34K99 Functional-differential equations (including equations with delayed, advanced or state-dependent argument) 34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations 34A40 Differential inequalities involving functions of a single real variable
##### Keywords:
first-order functional-differential inequalities
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##### References:
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