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**Properties of third-order nonlinear functional differential equations with mixed arguments.**
*(English)*
Zbl 1217.34109

Summary: The aim of this paper is to offer sufficient conditions for property (B) and/or the oscillation of the third-order nonlinear functional differential equation with mixed arguments

\[ [a(t)[x''(t)]^\gamma]'=q(t)f(x[\tau(t)])+p(t)h(x[\sigma(t)]). \]

Both cases \(\int^\infty a^{-1/\gamma}(s)\, ds=\infty\) and \(\int^\infty a^{-1/\gamma}(s)\, ds<\infty\) are considered. We deduce properties of the studied equations via new comparison theorems. The results obtained essentially improve and complement earlier ones.

\[ [a(t)[x''(t)]^\gamma]'=q(t)f(x[\tau(t)])+p(t)h(x[\sigma(t)]). \]

Both cases \(\int^\infty a^{-1/\gamma}(s)\, ds=\infty\) and \(\int^\infty a^{-1/\gamma}(s)\, ds<\infty\) are considered. We deduce properties of the studied equations via new comparison theorems. The results obtained essentially improve and complement earlier ones.

### MSC:

34K11 | Oscillation theory of functional-differential equations |

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\textit{B. Baculíková}, Abstr. Appl. Anal. 2011, Article ID 857860, 15 p. (2011; Zbl 1217.34109)

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### References:

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