@Article{ElAmrouss2021,
author = "El Amrouss, Abdelrachid and Hammouti, Omar",
title = "Spectrum of discrete 2n-th order difference operator with periodic boundary conditions and its applications",
journal = "Opuscula Math.",
year = "2021",
volume = "41",
number = "4",
pages = "489--507",
doi = "https://doi.org/10.7494/OpMath.2021.41.4.489",
url = "https://doi.org/10.7494/OpMath.2021.41.4.489",
abstract = "Let \(n\in\mathbb{N}^{*}\), and \(N\geq n\) be an integer. We study the spectrum of discrete linear \(2n\)-th order eigenvalue problems \[\begin{cases}\sum_{k=0}^{n}(-1)^{k}\Delta^{2k}u(t-k) = \lambda u(t) ,\quad & t\in[1, N]_{\mathbb{Z}}, \\ \Delta^{i}u(-(n-1))=\Delta^{i}u(N-(n-1)),\quad & i\in[0, 2n-1]_{\mathbb{Z}},\end{cases}\] where \(\lambda\) is a parameter. As an application of this spectrum result, we show the existence of a solution of discrete nonlinear \(2n\)-th order problems by applying the variational methods and critical point theory.",
keywords = "discrete boundary value problems, 2n-th order, variational methods, critical point theory",
issn = "1232-9274"
}