Leighton–Wintner-type oscillation theorem for the discrete [formula omitted]-Laplacian

Abstract

This paper addresses oscillation problems for difference equations with a discrete p(k)-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(k) diverges to infinity.