Multiple periodic solutions for second-order discrete Hamiltonian systems

Multiple periodic solutions for second-order discrete Hamiltonian systems

“…From the main conclusion, that is, Theorem 1.1 and Theorem 1.2, our results complete and extend some results that of in [11,16]. In the last, we would like to point out that based on the results reported in [1,7,12,13] on fractional calculus and time scales we will study some interesting problems, for example, the fractional Hamiltonian system on time scales.…”

“…Recently, in [16], under ∇G(t, u) satisfies (1.2), G is coercive or resonant and periodic only in a part of the variables, that is, there exists an integer k ∈ [0, N] such that:…”

“…Motivated by [6,11,[14][15][16], especially by [11,16], one natural question is: What will happen when ∇G is growing linearly and G is coercive or resonant and periodic only in a part of the variables? More concretely, can we obtain some results similar to that of in [16] with ∇G is growing linearly? It seems one interesting question.…”

Existence of periodic solutions for a class of second-order discrete Hamiltonian systems

“…Che and Xue [3] They obtained the existence of infinitely many periodic solutions of (1.2) by using the variant fountain theorem under the superquadratic assumptions (see Theorem 1.2 of [15]). Motivated by Che and Xue [3], Yan et al [13] and Zhang and Liu [15], we will discuss system (1.1) by the variant fountain theorem. We assume that Vðt; uðtÞÞ has the same form like (1.3) where UðÁÞ is a T-periodic symmetric matrix and W : R £ R N !…”

“…The critical point theory has been a powerful tool in dealing with the existence and multiplicity of periodic solutions, see [7] and [10]. Yan et al [13] investigated system (1.1) under the subquadratic potential function by using the generalized saddle point theorem. Che and Xue [3] They obtained the existence of infinitely many periodic solutions of (1.2) by using the variant fountain theorem under the superquadratic assumptions (see Theorem 1.2 of [15]).…”