Analytic Solutions of n-th Order Differential Equations at a Singular Point
| dc.contributor.author | Haile, Brian | |
| dc.date.accessioned | 2020-07-13T20:26:37Z | |
| dc.date.available | 2020-07-13T20:26:37Z | |
| dc.date.issued | 2002-02-04 | |
| dc.description.abstract | Necessary and sufficient conditions are be given for the existence of analytic solutions of the nonhomogeneous n-th order differential equation at a singular point. Let L be a linear differential operator with coefficients analytic at zero. If L* denotes the operator conjugate to L, then we will show that the dimension of the kernel of L is equal to the dimension of the kernel of L*. Certain representation theorems from functional analysis will be used to describe the space of linear functionals that contain the kernel of L*. These results will be used to derive a form of the Fredholm Alternative that will establish a link between the solvability of Ly = g at a singular point and the kernel of L*. The relationship between the roots of the indicial equation associated with and the kernel of L* will allow us to show that the kernel of L* is spanned by a set of polynomials. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 14 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Haile, B. (2002). Analytic solutions of n-th order differential equations at a singular point. <i>Electronic Journal of Differential Equations, 2002</i>(12), pp. 1-14. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/12052 | |
| dc.language.iso | en | |
| dc.publisher | Southwest Texas State University, Department of Mathematics | |
| dc.rights | Attribution 4.0 International | |
| dc.rights.holder | This work is licensed under a Creative Commons Attribution 4.0 International License. | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
| dc.source | Electronic Journal of Differential Equations, 2002, San Marcos, Texas: Southwest Texas State University and University of North Texas. | |
| dc.subject | Linear differential equation | |
| dc.subject | Regular singular point | |
| dc.subject | Analytic solution | |
| dc.title | Analytic Solutions of n-th Order Differential Equations at a Singular Point | |
| dc.type | Article |