Oscillation of second-order quasilinear retarded difference equations via canonical transform

Abstract

We study the oscillatory behavior of the second-order quasi-linear retarded difference equation \Delta(p(n)(\Delta y(n))^\alpha)+\eta(n) y^\beta(n- k)=0 under the condition $\sum_{n=n_0}^\infty p^{-\frc1{\alpha}}(n)<\infty$ (i.e., the noncanonical form). Unlike most existing results, the oscillatory behavior of this equation is attained by transforming it into an equation in the canonical form. Examples are provided to show the importance of our main results.

Keywords

• quasi-linear
• difference equation
• retarded
• second-order
• oscillation