Anti-periodic solutions for a higher order difference equation with \(p\)-Laplacian. (English) Zbl 1386.39002
Summary: A higher order difference equation is studied. The equation is defined on \(\mathbb{Z}\) and contains a \(p\)-Laplacian and both advance and retardation. Some criteria are established for the existence of infinitely many anti-periodic solutions of the equation. Several consequences of the main theorems are also included. Two examples are provided to illustrate the applicability of the results.
MSC:
| 39A05 | General theory of difference equations |
| 47J30 | Variational methods involving nonlinear operators |
| 58E05 | Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces |
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