Browsing by Subject "discrete boundary value problems"

Now showing 1 - 2 of 2

Access status: Open Access ,
On the dependence on parameters for second order discrete boundary value problems with the p(k)-Laplacian
(2014) Smejda, Joanna; Wieteska, Renata
In this paper we study the existence and the nonexistence of solutions for the boundary value problems of a class of nonlinear second-order discrete equations depending on a parameter. Variational (the mountain pass technique) and non-variational methods are applied.
Access status: Open Access ,
Spectrum of discrete 2n-th order difference operator with periodic boundary conditions and its applications
(Wydawnictwa AGH, 2021) El Amrouss, Abdelrachid; Hammouti, Omar
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.