Leighton–Wintner-type oscillation theorem for the discrete p(k)-Laplacian

Abstract

This paper addresses oscillation problems for difference equations with a discrete $p\left(k\right)$-Laplacian. In general, applying the Riccati technique to discrete oscillations is difficult. However, this study established a Leighton–Wintner-type oscillation theorem using the Riccati technique. Three examples are provided to illustrate the results. In particular, we examined the oscillatory problem for a certain nonlinear difference equation, including the Harper model, and demonstrated that the solutions are oscillatory even when $p\left(k\right)$ diverges to infinity.