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

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

Fasciculi Mathematici

2007

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.

Necessary and sufficient conditions for oscillation of solutions of a first order forced nonlinear difference equation with several delays

Rath R. N., Padhy L. N.

Fasciculi Mathematici

2005

Nr 35

99-113

In this paper necessary and sufficient conditions have been obtained so that every solution of the Neutral Delay Difference Equation (NDDE) oscillates or tends to zero as n —> &infin for different ranges of This paper improves and generalizes some recent work [2. 6, 8]. The results of this paper hold for linear, sublinear and superlinear equations and also for homogeneous equations, i.e. when fn ≡ 0.