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Spectrum of discrete 2n-th order difference operator with periodic boundary conditions and its applications

El Amrouss Abdelrachid, Hammouti Omar

Opuscula Mathematica

2021

Vol. 41, no. 4

489--507

Let n ∈ N*, and N ≥ n be an integer. We study the spectrum of discrete linear 2n-th order eigenvalue problems [formula] where λ 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.

On the dependence on parameters for second order discrete boundary value problems with the p(k)-Laplacian

Smejda J., Wieteska R.

Opuscula Mathematica

2014

Vol. 34, no. 4

851--870

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.