Cabada Fernández, AlbertoDimitrov, Nikolay2026-01-272026-01-272017-07-01Alberto CABADA, Nikolay D. DIMITROV, Existence of solutions of nonlocal perturbations of dirichlet discrete nonlinear problems, Acta Mathematica Scientia, Volume 37, Issue 4, 2017, Pages 911-926, ISSN 0252-9602, https://doi.org/10.1016/S0252-9602(17)30047-4.0252-9602https://hdl.handle.net/10347/45455This version of the article has been accepted for publication, after peer review and is subject to Springer Nature’s AM terms of use, but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: https://doi.org/10.1016/S0252-9602(17)30047-4This paper is devoted to the study of second order nonlinear difference equations. A Nonlocal Perturbation of a Dirichlet Boundary Value Problem is considered. An exhaustive study of the related Green's function to the linear part is done. The exact expression of the function is given, moreover the range of parameter for which it has constant sign is obtained. Using this, some existence results for the nonlinear problem are deduced from monotone iterative techniques, the classical Krasnoselski fixed point theorem or by application of recent fixed point theorems that combine both theories.engAttribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0/Dirichlet boundary value problemNonlocal perturbationsGreen's functionParameter dependence1202 Análisis y análisis funcionaljournal article10.1016/S0252-9602(17)30047-41572-9087open access