Cabada Fernández, AlbertoDimitrov, Nikolay2024-11-252024-11-252020-01Cabada, A., Dimitrov, N. Existence of Solutions of nth-Order Nonlinear Difference Equations with General Boundary Conditions. Acta Math Sci 40, 226–236 (2020). https://doi.org/10.1007/s10473-020-0115-y0252-960210.1007/s10473-020-0115-yhttps://hdl.handle.net/10347/37806This 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/10.1007/s10473-020-0115-yThe aim of this paper is to prove the existence of one or multiple solutions of nonlinear difference equations coupled to a general set of boundary conditions. Before to do this, we construct a discrete operator whose fixed points coincide with the solutions of the problem we are looking for. Moreover, we introduce a strong positiveness condition on the related Green's function that allows us to construct suitable cones where to apply adequate fixed point theorems. Once we have the general existence result, we deduce, as a particular case, the existence of solutions of a second order difference equation with nonlocal perturbed Dirichlet conditions.engAttribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0/Difference equationMultiplicity of solutionsGreen's functionPositive solutionsParameter dependence120207 Ecuaciones en diferenciasjournal article1572-9087open access