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Oscillation criteria for certain even order differential equations with distributed deviating arguments. (English) Zbl 1222.34082

Oscillation properties of the following even order differential equation with distributed deviating arguments
\[ \left( r(t)\left | x^{(n-1)}(t)\right | ^{p-1}x^{(n-1)}(t)\right) ^{\prime }+\int_{\alpha }^{\beta }F\left[ t,\xi ,x(g(t,\xi ))\right]\, d\sigma (\xi )=0, \]
\(a\) even, are investigated. The authors obtain Kamenev-type and interval oscillation criteria. In the proofs, Kiguradze’s lemma [I. T. Kiguradze, Mat. Sb., N. Ser. 65(107), 172–187 (1964; Zbl 0135.14302)] and Koplatadze’s lemma [R. Koplatadze, Mem. Differ. Equ. Math. Phys. 3 (1994; Zbl 0843.34070 ] are used. Two illustrative examples are given.

MSC:

34K11 Oscillation theory of functional-differential equations
34K40 Neutral functional-differential equations
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