## Differential and Integral Equations

### Positive homoclinic solutions for the discrete $p$-Laplacian with a coercive weight function

#### Abstract

We study a $p$-Laplacian difference equation on the set of integers, involving a coercive weight function and a reaction term satisfying the Ambrosetti--Rabinowitz condition. By means of critical-point theory and a discrete maximum principle, we prove the existence of a positive homoclinic solution.

#### Article information

Source
Differential Integral Equations, Volume 27, Number 1/2 (2014), 35-44.

Dates
First available in Project Euclid: 12 November 2013

Iannizzotto, Antonio; Rădulescu, Vicenţiu D. Positive homoclinic solutions for the discrete $p$-Laplacian with a coercive weight function. Differential Integral Equations 27 (2014), no. 1/2, 35--44. https://projecteuclid.org/euclid.die/1384282852