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Oscillation and non-oscillation of neutral difference equations of first order with positive and negative coefficients

100%

Rath R. , Padhy L. N. , Misra N.

Fasciculi Mathematici

2007

tom Nr 37

57-65

In this paper necessary and sufficient conditions have been obtained so that every solution of the Neutral Delay Difference Equation (NODE) where different symbols have there usual meaning, oscillates or tends to zero as n → infin for different ranges of {pn}- This paper generalizes some recent work. The results of this paper hold for linear, sublinear or super linear equations and also for homogeneous equations, i.e. when fn equiv 0.

Oscillation criteria for higher order neutral difference equations with oscillating coefficient

88%

Migda M.

Fasciculi Mathematici

2010

tom Nr 44

85-93

In this paper sufficient conditions for oscillation of all bounded solutions of the equation ...[wzór] where m ≥ 2, (pn) is an oscillatory sequence of real numbers, limn→∞ pn = 0, τ and σ are positive integers, f : N×R×R → R are established.

Existence criteria for positive solutions of a nonlinear difference inequality

75%

Cheng S. S. , Zhang G.

2000

tom 73

nr 3

197-220

This paper is concerned with a class of nonlinear difference inequalities which include many different classes of difference inequalities and equations as special cases. By means of a Riccati type transformation, necessary and sufficient conditions for the existence of eventually positive solutions and positive nonincreasing solutions are obtained. Various type of comparison theorems are also derived as applications, which extends many theorems in the literature.

Oscillation criteria for higher order functional difference equation with oscillating coeffcient

63%

Bolat Y.

2007

tom Vol. 40, nr 1

161-168

In this paper we are concerned with the oscillatory behaviour of solutions of a certain higher order nonlinear neutral type functional difference equation with oscillating coefficient. We obtain two sufficient criteria for oscillatory behaviour.