Cabada Fernández, AlbertoFernández Tojo, Fernando Adrián2026-02-162026-02-162014-04-01Alberto Cabada, F. Adrián F. Tojo, Existence results for a linear equation with reflection, non-constant coefficient and periodic boundary conditions, Journal of Mathematical Analysis and Applications, Volume 412, Issue 1, 2014, Pages 529-546, ISSN 0022-247X, https://doi.org/10.1016/j.jmaa.2013.10.067. (https://www.sciencedirect.com/science/article/pii/S0022247X13009839)0022-247Xhttps://hdl.handle.net/10347/45928This work is devoted to the study of first order linear problems with involution and periodic boundary value conditions. We first prove a correspondence between a large set of such problems with different involutions to later focus our attention to the case of the reflection. We study then different cases for which a Greenʼs function can be obtained explicitly and derive several results in order to obtain information about its sign. Once the sign is known, maximum and anti-maximum principles follow. We end this work with more general existence and uniqueness of solution resultsengAttribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0/Equations with involutionsEquations with reflectionGreenʼs functionsMaximum principlesComparison principlesPeriodic conditions1202 Análisis y análisis funcionaljournal article10.1016/j.jmaa.2013.10.0671096-0813open access