Analysis of singular one-dimensional linear boundary value problems using two-point taylor expansions

Ferreira, C. (Universidad de Zaragoza) ; López, J.L. ; Perez Sinusía, E. (Universidad de Zaragoza)

Resumen: We 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.

Idioma: Inglés

DOI: 10.14232/ejqtde.2020.1.22

Año: 2020

Publicado en: Electronic Journal of Qualitative Theory of Differential Equations 22 (2020), [21 pp.]
ISSN: 1417-3875

Factor impacto JCR: 1.874 (2020)

Categ. JCR: MATHEMATICS rank: 44 / 330 = 0.133 (2020) - Q1 - T1
Categ. JCR: MATHEMATICS, APPLIED rank: 85 / 265 = 0.321 (2020) - Q2 - T1

Factor impacto SCIMAGO: 0.524 - Applied Mathematics (Q2)

Financiación: info:eu-repo/grantAgreement/ES/DGA-FSE/E24-17R
Financiación: info:eu-repo/grantAgreement/ES/MINECO/MTM2017-83490-P

Tipo y forma: Artículo (PostPrint)

Área (Departamento): Área Matemática Aplicada (Dpto. Matemática Aplicada)