Cabada Fernández, AlbertoIannizzotto, Antonio2026-02-162026-02-162013-11-01Alberto Cabada, Antonio Iannizzotto, Existence of homoclinic constant sign solutions for a difference equation on the integers, Applied Mathematics and Computation, Volume 224, 2013, Pages 216-223, ISSN 0096-3003, https://doi.org/10.1016/j.amc.2013.08.017. (https://www.sciencedirect.com/science/article/pii/S0096300313008667)0096-3003https://hdl.handle.net/10347/45926We consider a difference equation involving the discrete $p$-Laplacian operator, depending on a positive real parameter $\lambda$. We prove, under convenient assumptions, that for $\lambda$ big enough the equations admits at least one homoclinic constant sign solution in $\Z$. Our method consists in two parts: first, we prove the existence of two Dirichlet-type solutions for the equation in the discrete interval $[-n,n]$, for all $n\in\N$ big enough; then, we show that such solutions converge to a homoclinic solution in $\Z$, as $n\to\infty$engAttribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0/Difference equationsDiscrete p-LaplacianVariational methods1202 Análisis y análisis funcionaljournal article10.1016/j.amc.2013.08.0171873-5649open access