Abstract
In this paper, we deal with the second order discrete Hamiltonian system $\Delta[p(n) \Delta u(n-1)] - L(n) u(n) + \nabla W(n,u(n)) = 0$, where $L\colon \mathbb{Z} \to \mathbb{R}^{N \times N}$ is positive definite for sufficiently large $|n| \in \mathbb{Z}$ and $W(n,x)$ is indefinite sign. By using critical point theory, we establish some new criteria to guarantee that the above system has infinitely many nontrivial homoclinic solutions under the assumption that $W(n,x)$ is asymptotically quadratic and supquadratic, respectively. Our results generalize and improve some existing results in the literature.
Citation
Huiwen Chen. Zhimin He. Jianli Li. Zigen Ouyang. "New Results for Second Order Discrete Hamiltonian Systems." Taiwanese J. Math. 21 (2) 403 - 428, 2017. https://doi.org/10.11650/tjm/7762
Information