In this paper, we introduce a variational framework to a fractional difference equation on $\mathbb{Z}$ driven by the fractional discrete Laplacian and involving a coercive weight function and a positive parameter $\lambda$. By means of the critical point theory, we prove the existence of at least two nontrivial and nonnegative homoclinic solutions for $\lambda$ big enough.

中文翻译：

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分数阶离散拉普拉斯方程的同宿解

在本文中，我们为分数差分方程引入了变分框架 $\mathbb{ž}$ 由分数离散拉普拉斯算子驱动，并涉及矫顽权重函数和正参数 $\lambda$。通过临界点理论，我们证明了存在至少两个非平凡和非负同宿解$\lambda$ 足够大。