### Existence of solutions for nonlinear p-Laplacian difference equations

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.

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

### Refbacks

- There are currently no refbacks.