JournalszaaVol. 16, No. 3pp. 749–759

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

  • E. Thandapani

    University of Madras, Chennai, India
  • R. Arul

    Periyar University, Salem, India
Oscillation and Non-Oscillation Theorems for a Class of Second Order Quasilinear Difference Equations cover
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Abstract

In this paper there are established necesssary and sufficient conditions for the second order quasilinear difference equation

Δ(pnφ(Δyn))+f(n,yn+1)=0   (nN0)\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.

Cite this article

E. Thandapani, R. Arul, Oscillation and Non-Oscillation Theorems for a Class of Second Order Quasilinear Difference Equations. Z. Anal. Anwend. 16 (1997), no. 3, pp. 749–759

DOI 10.4171/ZAA/789