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arXiv · 1408.6016

Existence of homoclinic solution in first order discrete Hamiltonian system

Wenxiong Chen
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Abstract

In this paper we consider the first order discrete Hamiltonian system $$\begin{cases} x_1(n+1)-x_1(n)& =- H_{x_2}(n,x(n)), x_2(n)-x_2(n-1)& =\ \ H_{x_1}(n,x(n)). \end{cases} $$ Where $n\in \mathbb{Z}$, $x(n)=$ $x_1 (n) \choose x_2 (n)$$ \in \mathbb{R}^{2N}$, $ H(n,z)= \frac12S(n)z\cdot z + R(n,z)$ is periodic in $n$ and asymptotically quadratic as $|z| \to \infty$. We will prove the existence of homoclonic solution by critical point theorem for strongly indefinite functional.

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Wenxiong Chen. 2014-08-26. Existence of homoclinic solution in first order discrete Hamiltonian system. https://arxiv.org/abs/1408.6016

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