78710 20191126134630.0 doi 10.1016/j.jmaa.2018.03.041 sideral 105253 ART-2018-105253 eng (orcid)0000-0002-3698-6719 Ferreira, C. Universidad de Zaragoza The use of two-point Taylor expansions in singular one-dimensional boundary value problems I 2018 Access copy available to the general public Unrestricted We consider the second-order linear differential equation (x+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(x), g(x) and h(x) are analytic in a Cassini disk Dr with foci at x=±1 containing the interval [-1, 1]. Then, the end point of the interval x=-1 may be a regular singular point 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 approximation of the analytic solutions when they exist. info:eu-repo/grantAgreement/ES/MINECO/MTM2014-52859-P info:eu-repo/semantics/openAccess by-nc-nd http://creativecommons.org/licenses/by-nc-nd/3.0/es/ 1.188 2018 MATHEMATICS 65 / 313 = 0.208 2018 Q1 T1 MATHEMATICS, APPLIED 117 / 254 = 0.461 2018 Q2 T2 0.966 2018 Applied Mathematics 2018 Q2 Analysis 2018 Q2 info:eu-repo/semantics/article info:eu-repo/semantics/acceptedVersion López, J.L. (orcid)0000-0002-8021-2745 Pérez Sinusía, E. Universidad de Zaragoza 2005 595 Universidad de Zaragoza Dpto. Matemática Aplicada Área Matemática Aplicada 463, 2 (2018), 708-725 J. math. anal. appl. Journal of Mathematical Analysis and Applications 0022-247X 182799 http://zaguan.unizar.es/record/78710/files/texto_completo.pdf Postprint 78993 http://zaguan.unizar.es/record/78710/files/texto_completo.jpg?subformat=icon icon Postprint oai:zaguan.unizar.es:78710 articulos driver 2019-11-26-13:40:47 ARTICLE