TY  - JOUR
ID  - ElAmrouss2021
LB  - ElAmrouss2021
AU  - El Amrouss, Abdelrachid
AU  - Hammouti, Omar
TI  - Spectrum of discrete 2n-th order difference operator with periodic boundary conditions and its applications
ST  - Spectrum of discrete 2n-th order difference operator with periodic boundary conditions and its applications
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2021
VL  - 41
IS  - 4
SP  - 489
EP  - 507
DO  - https://doi.org/10.7494/OpMath.2021.41.4.489
UR  - https://doi.org/10.7494/OpMath.2021.41.4.489
AB  - 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.
KW  - discrete boundary value problems
KW  - 2n-th order
KW  - variational methods
KW  - critical point theory
SN  - 1232-9274
ER  -