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Zbl 1116.34050
Agarwal, Ravi P.; Grace, Said R.; Smith, Tim
Oscillation of certain third order functional differential equations. (English)
[J] Adv. Math. Sci. Appl. 16, No. 1, 69-94 (2006). ISSN 1343-4373

The authors consider third order functional differential equations of the form $$L_{3}x(t)+\delta q(t)f(x[g(t)])=0, $$ where $\delta=\pm 1$, $L_{0}x(t)=x(t)$, $L_{3}x(t)=\frac{d}{dt}L_{2}x(t)$, $L_{k}x(t)={1\over a_{k}(t)}\left(\frac{d}{dt}L_{k-1}x(t)\right)^{\alpha_{k}}, k=1, 2$. By discussing the nonexistence of some types of solutions to the above equations, they establish a number of new oscillation criteria for these equations. They also give three illustrative examples and apply the previous results to neutral equations of the form $$L_{3}(x(t)+p(t)x[\tau(t)])+\delta q(t)f(x[g(t)])=0.$$
[Qiru Wang (Guangzhou)]

MSC 2000:: *34K11 Oscillation theory of functional-differential equations

Keywords: nonoscillation; nonlinear; comparison

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Zentralblatt MATH Berlin [Germany]