doi:10.14232/ejqtde.2020.1.22engFerreira, C.López, J.L.Perez Sinusía, E.Analysis of singular one-dimensional linear boundary value problems using two-point taylor expansionsART-2020-117999We consider the second-order linear differential equation (x2 - 1)y'' + f (x)y' + g(x)y = h(x) in the interval (-1, 1) with initial conditions or boundary conditions (Dirichlet, Neumann or mixed Dirichlet–Neumann). The functions f, g and h are analytic in a Cassini disk Dr with foci at x = ±1 containing the interval [-1, 1]. Then, the two end points of the interval may be regular singular points of the differential equation. The two-point Taylor expansion of the solution y(x) at the end points ±1 is used to study the space of analytic solutions in Dr of the differential equation, and to give a criterion for the existence and uniqueness of analytic solutions of the boundary value problem. This method is constructive and provides the two-point Taylor appro-ximation of the analytic solutions when they exist.2020http://zaguan.unizar.es/record/16552410.14232/ejqtde.2020.1.22http://zaguan.unizar.es/record/165524oai:zaguan.unizar.es:165524info:eu-repo/grantAgreement/ES/DGA-FSE/E24-17Rinfo:eu-repo/grantAgreement/ES/MINECO/MTM2017-83490-PElectronic Journal of Qualitative Theory of Differential Equations 22 (2020), [21 pp.]by-nc-ndhttps://creativecommons.org/licenses/by-nc-nd/4.0/deed.esinfo:eu-repo/semantics/openAccess