Periodic solutions for second-order discrete Hamiltonian systems

Abstract

By using the least action principle and the minimax methods, some existence theorems are obtained for periodic solutions of second-order discrete Hamiltonian systems: e 2 uðn 2 1Þ ¼ 7Fðn; uðnÞÞ; n [ Z;in the cases where the nonlinearity 7Fðn; xÞ is growing sublinearly or linearly.

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.…”

“…Afterward, in [14,15], Xue and Tang studied the system (1.1), in which ∇G is growing sublinearly: there exist δ > 0, η > 0 satisfying In case ∇G is growing sublinearly or linearly (that is ∇G satisfies (1.2) with α = 1), Tang and Zhang [11] extended the main results obtained in [6,14,15] under more weakened conditions on G:…”

“…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?…”

Periodic solutions for discrete p ( k ) $p(k)$ -Laplacian systems with partially periodic potential

“…During the past decade, periodic solutions, subharmonic solutions, and homoclinic orbits for second order discrete Hamiltonian systems have captured special attention, and some solvability conditions have been given under distinct hypotheses on potential function [6][7][8][9][10][11][12][13].…”

Existence of periodic solutions for a class of discrete systems with classical or bounded (phi_1,phi_2)-Laplacian

“…It is impossible to review them one by one here. We just refer readers to [5,6,10,13,23,25,[27][28][29] and references therein. Recently, in [14] and [15], Mawhin studied a class of nonlinear discrete systems with φ-Laplacian which possesses generality.…”