Cabada Fernández, AlbertoDimitrov, Nikolay D.2020-04-022020-04-022019Cabada, A., Dimitrov, N.D. Nontrivial solutions of inverse discrete problems with sign-changing nonlinearities. Adv Differ Equ 2019, 450 (2019). https://doi.org/10.1186/s13662-019-2383-yhttp://hdl.handle.net/10347/21099This paper is concerned with the existence of solutions of an inverse discrete problem with sign-changing nonlinearity. This kind of problems includes, as a particular case, nth order difference equations coupled with suitable conditions on the boundary of the interval of definition. It would be valid for the case in which the related Green’s function is positive on a subset of its rectangle of definition. The existence results follow from spectral theory, as an application of the Krein–Rutman theorem and by means of degree theoryeng© The Author(s) 2019. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/),which permits unrestricted use, distribution, and reproduction in anymedium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were madehttp://creativecommons.org/licenses/by/4.0/Inverse discrete problemDifference equationGreen’s functionSpectral radiousjournal article10.1186/s13662-019-2383-y1687-1847open access