Ferreira Chelo and López José L. and Pérez Sinusía Ester: Analysis of singular one-dimensional linear boundary value problems using two-point Taylor expansions. (2020)
Preview |
Teljes mű
ejqtde_2020_022.pdf Download (371kB) | Preview |
Abstract
We consider the second-order linear differential equation (x 2 − 1)y 00 + f(x)y 0 + 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 approximation of the analytic solutions when they exist.
| Item Type: | Journal |
|---|---|
| Publication full: | Electronic journal of qualitative theory of differential equations |
| Date: | 2020 |
| Number: | 22 |
| ISSN: | 1417-3875 |
| Uncontrolled Keywords: | Differenciálegyenlet |
| Additional Information: | Bibliogr.: 21. p. ; összefoglalás angol nyelven |
| Date Deposited: | 2020. Jun. 08. 09:07 |
| Last Modified: | 2021. Oct. 20. 13:52 |
| URI: | http://acta.bibl.u-szeged.hu/id/eprint/69526 |
Actions (login required)
 |
View Item |
