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Solutions for discrete Schrödinger equations with a nonlocal term
Applied Mathematics Letters ( IF 2.9 ) Pub Date : 2020-11-27 , DOI: 10.1016/j.aml.2020.106930
Qilin Xie

In the present paper, we consider the following discrete Schrödinger equations m(kZ(|Δuk1|2+Vk|uk|2))(Δ2uk1+Vkuk)ωuk=fk(uk)kZ,where m is a continuous function and V={Vk} is a positive potential, ωR, Δuk1=ukuk1 and Δ2=Δ(Δ) is the one dimensional discrete Laplacian operator. Under some suitable assumptions on fk, we prove the existence of nontrivial solutions for this nonlocal problems by variation methods.



中文翻译:

具有非局部项的离散Schrödinger方程的解

在本文中,我们考虑以下离散Schrödinger方程在本文中,我们考虑以下离散Schrödinger方程 ķž|Δüķ-1个|2+Vķ|üķ|2-Δ2üķ-1个+Vķüķ-ωüķ=Fķüķķž哪里 是一个连续函数, V={Vķ} 是一个积极的潜力, ω[RΔüķ-1个=üķ-üķ-1个Δ2=ΔΔ是一维离散拉普拉斯算子。在一些适当的假设下Fķ,我们通过变分方法证明了该非局部问题非平凡解的存在。哪里 是一个连续函数, V={Vķ} 是一个积极的潜力, ω[RΔüķ-1个=üķ-üķ-1个Δ2=ΔΔ是一维离散拉普拉斯算子。在一些适当的假设下Fķ,我们通过变分方法证明了该非局部问题非平凡解的存在。

更新日期:2020-12-02
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