Cabada Fernández, AlbertoFernández Tojo, Fernando Adrián2026-02-192026-02-192013Cabada, A. and Tojo, F. A. Solutions of the first order linear equation with reflection and general linear conditions. In: Global Journal of Mathematical Sciences, Vol 2, No 1 (2013)https://hdl.handle.net/10347/45979This work is devoted to the study of first order linear problems with involution and general linear conditions. We first study the problem in the case of antiperiodic boundary conditions, giving an explicit Green's function for it. Then we move forward to more general linear boundary conditions, focusing on sufficient conditions for existence and uniqueness of solution. At the end of the paper we give estimates that ensure the positivity of the solution in the general problems and illustrate these applications with examplesengThis journal provides immediate open access to its content on the principle that making research freely available to the public supports a greater global exchange of knowledgeEquations with involutionsEquations with reflectionGreen’s functionsMaximum principlesComparison principlesPeriodic conditions1202 Análisis y análisis funcionaljournal article2164-3709open access