Oscillation for Quasilinear Difference Equations

Here, we shall consider the perturbed quasilinear difference equation 15.1 $$\Delta \left( {a\left( {k - 1} \right)|\Delta y\left( {k - 1} \right){|^{\sigma - 1}}\Delta y\left( {k - 1} \right)} \right) + A\left( {k,y\left( k \right)} \right) = B\left( {k,y\left( k \right),\Delta y\left( k \right)} \right),k \in N\left( 1 \right)$$ where σ > 0, and as in equation (14.1), the function a(k) is eventually positive, A : N(1) × ℝ → ℝ, B : N(1) × ℝ × ℝ → ℝ; and that there exist functions α(k), β(k), and f satisfying (12.2), (12.3) and (13.2). For the difference equation (15.1) we shall discuss results analogous to those presented in Section 14.