Liang Zhang, Xianhua Tang
Abstract:
In this article, we sutdy the multiplicity of homoclinic solutions to
the perturbed second-order discrete Hamiltonian system
![$$
\Delta[p(n)\Delta u(n-1)]-L(n)u(n)+\nabla W(n,u(n))+\theta\nabla F(n,u(n))=0,
$$](gifs/aa.gif)
where L(n) and W(n,x) are neither autonomous nor periodic in n.
Under the assumption that W(n,x) is only locally superquardic as
and even in x and F(n,x) is a perturbation term,
we establish some existence criteria to guarantee that the above system has
multiple homoclinic solutions by minimax method in critical point theory.
Submitted June 9, 2015. Published October 21, 2015.
Math Subject Classifications: 39A11, 58E05, 70H05.
Key Words: Critical point; discrete Hamilton system; homoclinic solution;
small perturbation
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Liang Zhang School of Mathematical Sciences University of Jinan Jinan 250022, China email: mathspaper2012@163.com |
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Xianhua Tang School of Mathematics and Statistics Central South University Changsha 410083, China email: tangxh@csu.edu.cn |
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