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

K. Fujimoto, K. Ishibashi and M. Onitsuka

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

Applied Mathematics Letters

163

109465

1

6

https://doi.org/10.1016/j.aml.2025.109465