### Oscillation criteria for high order delay partial differential equations.

Liu, Xinzhi, Fu, Xilin (1998)

Journal of Applied Mathematics and Stochastic Analysis

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Liu, Xinzhi, Fu, Xilin (1998)

Journal of Applied Mathematics and Stochastic Analysis

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N. Parhi (2000)

Czechoslovak Mathematical Journal

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In this paper, sufficient conditions have been obtained for oscillation of solutions of a class of $n$th order linear neutral delay-differential equations. Some of these results have been used to study oscillatory behaviour of solutions of a class of boundary value problems for neutral hyperbolic partial differential equations.

Satoshi Tanaka, Norio Yoshida (2005)

Annales Polonici Mathematici

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Certain hyperbolic equations with continuous distributed deviating arguments are studied, and sufficient conditions are obtained for every solution of some boundary value problems to be oscillatory in a cylindrical domain. Our approach is to reduce the multi-dimensional oscillation problems to one-dimensional oscillation problems for functional differential inequalities by using some integral means of solutions.

Jozef Džurina (2004)

Mathematica Slovaca

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Grace, S.R., Lalli, B.S. (1987)

International Journal of Mathematics and Mathematical Sciences

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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.

Tiryaki, Aydin (2009)

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

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