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Necessary and sufficient conditions for the oscillation of forced nonlinear second order delay difference equation

Ethiraju ThandapaniL. Ramuppillai — 1999

Kybernetika

In this paper the authors give necessary and sufficient conditions for the oscillation of solutions of nonlinear delay difference equations of Emden– Fowler type in the form Δ 2 y n - 1 + q n y σ ( n ) γ = g n , where γ is a quotient of odd positive integers, in the superlinear case ( γ > 1 ) and in the sublinear case ( γ < 1 ) .

On the oscillation of third-order quasi-linear neutral functional differential equations

Ethiraju ThandapaniTongxing Li — 2011

Archivum Mathematicum

The aim of this paper is to study asymptotic properties of the third-order quasi-linear neutral functional differential equation [ a ( t ) ( [ x ( t ) + p ( t ) x ( δ ( t ) ) ] ' ' ) α ] ' + q ( t ) x α ( τ ( t ) ) = 0 , E where α > 0 , 0 p ( t ) p 0 < and δ ( t ) t . By using Riccati transformation, we establish some sufficient conditions which ensure that every solution of () is either oscillatory or converges to zero. These results improve some known results in the literature. Two examples are given to illustrate the main results.

Oscillatory and asymptotic behaviour of perturbed quasilinear second order difference equations

Ethiraju ThandapaniL. Ramuppillai — 1998

Archivum Mathematicum

This paper deals with oscillatory and asymptotic behaviour of solutions of second order quasilinear difference equation of the form Δ ( a n - 1 | Δ y n - 1 | α - 1 Δ y n - 1 ) + F ( n , y n ) = G ( n , y n , Δ y n ) , n N ( n 0 ) ( E ) where α > 0 . Some sufficient conditions for all solutions of (E) to be oscillatory are obtained. Asymptotic behaviour of nonoscillatory solutions of (E) are also considered.

Oscillation of third-order delay difference equations with negative damping term

Martin BohnerSrinivasan GeethaSrinivasan SelvarangamEthiraju Thandapani — 2018

Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica

The aim of this paper is to investigate the oscillatory and asymptotic behavior of solutions of a third-order delay difference equation. By using comparison theorems, we deduce oscillation of the difference equation from its relation to certain associated first-order delay difference equations or inequalities. Examples are given to illustrate the main results.

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