Spectrum of discrete 2n-th order difference operator with periodic boundary conditions and its applications
Keyword(s):
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.
1978 ◽
Vol 80
(3-4)
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pp. 357-362
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2009 ◽
Vol 198
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pp. 2246-2259
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Keyword(s):
2021 ◽
1994 ◽
Vol 111
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pp. 74-80
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2001 ◽
Vol 121
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pp. 1-15
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1991 ◽
Vol 14
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pp. 127-137
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