López Somoza, LucíaMinhós, Feliz2019-10-242019-10-242019López-Somoza, L., & Minhós, F. (2019). On multipoint resonant problems on the half-line. Boundary Value Problems, 2019(1). doi: 10.1186/s13661-019-1153-9http://hdl.handle.net/10347/19926In this work we obtain sufficient conditions for the existence of bounded solutions of a resonant multipoint second-order boundary value problem, with a fully differential equation. The noninvertibility of the linear part is overcome by a new perturbation technique, which allows obtaining an existence result and a localization theorem. Our hypotheses are clearly much less restrictive than those existent in the literature and, moreover, they can be applied to higher-order, resonant or nonresonant, boundary value problems defined on the half-line or even on the real lineeng© 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 any medium, 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/Multipoint problemsUnbounded domainsResonant problemsjournal article10.1186/s13661-019-1153-91687-2770open access