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Zeitschrift für Analysis und ihre Anwendungen


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Volume 16, Issue 3, 1997, pp. 749–759
DOI: 10.4171/ZAA/789

Published online: 1997-09-30

Oscillation and Non-Oscillation Theorems for a Class of Second Order Quasilinear Difference Equations

E. Thandapani[1] and R. Arul[2]

(1) University of Madras, Chennai, India
(2) Periyar University, Salem, India

In this paper there are established necesssary and sufficient conditions for the second order quasilinear difference equation $$\Delta(p_n \varphi (\Delta y_n)) + f(n,y_{n+1}) = 0 \ \ \ (n \in \mathbb N_0)$$ to have various types of non-oscillatory solutions. In addition, in the case that the equation is either strongly superlinear or strongly sublinear, there are established necessary and sufficient conditions for all solutions to oscillate.

Keywords: Quasilinear difference equations, oscillation, non-oscillatory solutions

Thandapani E., Arul R.: Oscillation and Non-Oscillation Theorems for a Class of Second Order Quasilinear Difference Equations. Z. Anal. Anwend. 16 (1997), 749-759. doi: 10.4171/ZAA/789