Existence of solutions for nonlinear p-Laplacian difference equations

Lorena Saavedra, Stepan Tersian

DOI: http://dx.doi.org/10.12775/TMNA.2017.022

Abstract


The aim of this paper is the study of existence of solutions for
nonlinear $2n^{\mathrm{th}}$-order difference equations involving
$p$-Laplacian. In the first part, the existence of a nontrivial
homoclinic solution for a discrete $p$-Laplacian problem is proved.
The proof is based on the mountain-pass theorem of Brezis and
Nirenberg. Then, we study the existence of multiple solutions for a
discrete $p$-Laplacian boundary value problem. In this case the
proof is based on the three critical points theorem of Averna and
Bonanno.

Keywords


$p$-Laplacian; difference equations; mountain-pass theorem

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