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Existence of periodic solutions for a class of asymptotically \(p\)-linear discrete systems involving \(p\)-Laplacian. (English) Zbl 1247.35030

Summary: By applying the mountain pass theorem in critical point theory, two existence results are obtained for the following asymptotically \(p\)-linear \(p\)-Laplacian discrete system: \(\Delta(|\Delta u(t - 1)|^{p-2} \Delta u(t - 1)) + \nabla[-K(t, u(t)) + W(t, u(t))] = 0\). The results obtained generalize some known works.

MSC:

35J48 Higher-order elliptic systems
35B09 Positive solutions to PDEs
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