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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

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
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