Cabada Fernández, AlbertoFernández Tojo, Fernando Adrián2018-06-292018-06-292014Cabada, A. & Tojo, F.A.F. Bound Value Probl (2014) 2014: 99. https://doi.org/10.1186/1687-2770-2014-9910.1186/1687-2770-2014-99http://hdl.handle.net/10347/16906This work is devoted to the study of the existence and sign of Green’s functions for first order linear problems with constant coefficients and initial (one point) conditions. We first prove a result on the existence of solutions of nth order linear equations with involutions via some auxiliary functions to later prove a uniqueness result in the first order case. We study then different situations for which a Green’s function can be obtained explicitly and derive several results in order to obtain information as regards the sign of the Green’s function. Once the sign is known, optimal maximum and anti-maximum principles followeng© Cabada and Tojo; licensee Springer. 2014 This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly creditedhttp://creativecommons.org/licenses/by/2.0Equations with involutionsEquations with reflectionGreen's functionsMaximum principlesComparison principloesPeriodic conditionsjournal article1687-2770open access