Displaying similar documents to “Asymptotic properties of nonoscillatory solutions of neutral delay differential equations of n -th order”

Comparison theorems for functional differential equations

Jozef Džurina (1994)

Mathematica Bohemica

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In this paper the oscillatory and asymptotic properties of the solutions of the functional differential equation L n u ( t ) + p ( t ) f ( u [ g ( t ) ] ) = 0 are compared with those of the functional differential equation α n u ( t ) + q ( t ) h ( u [ w ( t ) ] ) = 0 .

Oscillation of a higher order neutral differential equation with a sub-linear delay term and positive and negative coefficients

Julio G. Dix, Dillip Kumar Ghose, Radhanath Rath (2009)

Mathematica Bohemica

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We obtain sufficient conditions for every solution of the differential equation [ y ( t ) - p ( t ) y ( r ( t ) ) ] ( n ) + v ( t ) G ( y ( g ( t ) ) ) - u ( t ) H ( y ( h ( t ) ) ) = f ( t ) to oscillate or to tend to zero as t approaches infinity. In particular, we extend the results of Karpuz, Rath and Padhy (2008) to the case when G has sub-linear growth at infinity. Our results also apply to the neutral equation [ y ( t ) - p ( t ) y ( r ( t ) ) ] ( n ) + q ( t ) G ( y ( g ( t ) ) ) = f ( t ) when q ( t ) has sign changes. Both bounded and unbounded solutions are consideted here; thus some known results are expanded.

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.