Oscillation and non-oscillation in solutions of nonlinear stochastic delay differential equations.

Appleby, John A.D.; Kelly, Cónall

Displaying similar documents to “Oscillation and non-oscillation in solutions of nonlinear stochastic delay differential equations.”

Oscillation of second order neutral delay differential equations

J. Džurina, D. Hudáková (2009)

Mathematica Bohemica

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We establish some new oscillation criteria for the second order neutral delay differential equation ${[r (t) | [x (t) + p (t) x [τ (t)]]}^{'} {|^{α - 1} {[x (t) + p (t) x [τ (t)]]}^{'}]}^{'} + q (t) f (x [σ (t)]) = 0 .$ The obtained results supplement those of Dzurina and Stavroulakis, Sun and Meng, Xu and Meng, Baculíková and Lacková. We also make a slight improvement of one assumption in the paper of Xu and Meng.

Oscillation criteria for second-order delay, difference, and functional equations.

Kikina, L.K., Stavroulakis, I.P. (2010)

International Journal of Differential Equations

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Oscillation criteria of third-order nonlinear delay differential equations

Samir H. Saker (2006)

Mathematica Slovaca

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Oscillation criteria for second-order superlinear neutral differential equations.

Li, Tongxing, Han, Zhenlai, Zhang, Chenghui, Li, Hua (2011)

Abstract and Applied Analysis

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Oscillation theorems for certain even order neutral differential equations

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 $\frac{d}{d t} (| {(x (t) + p (t) x (τ (t)))}^{(n - 1)} |^{α - 1} {(x (t) + p (t) x (τ (t)))}^{(n - 1)}) + F (t, x (g (t))) = 0,$ where $n$ is even and $t \geq t_{0}$ . 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.

Comparison theorems for the third-order delay trinomial differential equations.

Baculíková, B., Džurina, J. (2010)

Advances in Difference Equations [electronic only]

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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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Oscillation of second-order linear delay differential equations

Ján Ohriska (2008)

Open Mathematics

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The aim of this paper is to derive sufficient conditions for the linear delay differential equation (r(t)y′(t))′ + p(t)y(τ(t)) = 0 to be oscillatory by using a generalization of the Lagrange mean-value theorem, the Riccati differential inequality and the Sturm comparison theorem.