Displaying similar documents to “Oscillation of Volterra integral equations and forced functional differential equations.”

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 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 ≥ 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.

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.