### Oscillation criteria for a certain second-order nonlinear differential equations with deviating arguments.

Tiryaki, Aydin (2009)

Electronic Journal of Qualitative Theory of Differential Equations [electronic only]

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Tiryaki, Aydin (2009)

Electronic Journal of Qualitative Theory of Differential Equations [electronic only]

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Eva Špániková (2004)

Archivum Mathematicum

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We study oscillatory properties of solutions of the systems of differential equations of neutral type.

Qi Gui Yang, Sui-Sun Cheng (2007)

Archivum Mathematicum

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This paper is concerned with a class of even order nonlinear differential equations of the form $$\frac{d}{dt}\left(|{\left(x\left(t\right)+p\left(t\right)x\left(\tau \right(t\left)\right)\right)}^{(n-1)}{|}^{\alpha -1}{(x\left(t\right)+p\left(t\right)x\left(\tau \left(t\right)\right))}^{(n-1)}\right)+F(t,x\left(g\left(t\right)\right))=0\phantom{\rule{0.166667em}{0ex}},$$ where $n$ is even and $t\ge {t}_{0}$. By using the generalized Riccati transformation and the averaging technique, new oscillation criteria are obtained which are either extensions of or complementary to a number of existing results. Our results are more general and sharper than some previous results even for second order equations.

Zhang, Siyu, Meng, Fanwei (2010)

International Journal of Differential Equations

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Blanka Baculíková (2006)

Archivum Mathematicum

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Our aim in this paper is to present criteria for oscillation of the nonlinear differential equation $${u}^{\text{'}\text{'}}\left(t\right)+p\left(t\right)f\left(u\left(g\left(t\right)\right)\right)=0\phantom{\rule{0.166667em}{0ex}}.$$ The obtained oscillatory criteria improve existing ones.