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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.

MSC:
34K11Oscillation theory of functional-differential equations
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References:
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