Infinitely Many Eigenfunctions for Polynomial Problems: Exact Results
Let Fx, y=asxys+as-1xys-1+⋯+a0x be a real-valued polynomial function in which the degree s of y in Fx, y is greater than or equal to 1. For any polynomial yx, we assume that T:Rx→Rx is a nonlinear operator with Tyx=Fx, yx. In this paper, we will find an eigenfunction yx∈Rx to satisfy the following e...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2015-01-01
|
| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2015/516159 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832548910904639488 |
|---|---|
| author | Yi-Chou Chen |
| author_facet | Yi-Chou Chen |
| author_sort | Yi-Chou Chen |
| collection | DOAJ |
| description | Let Fx, y=asxys+as-1xys-1+⋯+a0x be a real-valued polynomial function in which the degree s of y in Fx, y is greater than or equal to 1. For any polynomial yx, we assume that T:Rx→Rx is a nonlinear operator with Tyx=Fx, yx. In this paper, we will find an eigenfunction yx∈Rx to satisfy the following equation: Fx, yx=ayx for some eigenvalue a∈R and we call the problem Fx, yx=ayx a fixed point like problem. If the number of all eigenfunctions in Fx, yx=ayx is infinitely many, we prove that (i) any coefficients of Fx, y, asx, as-1x,…, a0x, are all constants in R and (ii) yx is an eigenfunction in Fx, yx=ayx if and only if yx∈R. |
| format | Article |
| id | doaj-art-b3ce7119b3f54612be323f417aabdde4 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-b3ce7119b3f54612be323f417aabdde42025-02-03T06:12:42ZengWileyJournal of Applied Mathematics1110-757X1687-00422015-01-01201510.1155/2015/516159516159Infinitely Many Eigenfunctions for Polynomial Problems: Exact ResultsYi-Chou Chen0Department of General Education, National Army Academy, Taoyuan 320, TaiwanLet Fx, y=asxys+as-1xys-1+⋯+a0x be a real-valued polynomial function in which the degree s of y in Fx, y is greater than or equal to 1. For any polynomial yx, we assume that T:Rx→Rx is a nonlinear operator with Tyx=Fx, yx. In this paper, we will find an eigenfunction yx∈Rx to satisfy the following equation: Fx, yx=ayx for some eigenvalue a∈R and we call the problem Fx, yx=ayx a fixed point like problem. If the number of all eigenfunctions in Fx, yx=ayx is infinitely many, we prove that (i) any coefficients of Fx, y, asx, as-1x,…, a0x, are all constants in R and (ii) yx is an eigenfunction in Fx, yx=ayx if and only if yx∈R.http://dx.doi.org/10.1155/2015/516159 |
| spellingShingle | Yi-Chou Chen Infinitely Many Eigenfunctions for Polynomial Problems: Exact Results Journal of Applied Mathematics |
| title | Infinitely Many Eigenfunctions for Polynomial Problems: Exact Results |
| title_full | Infinitely Many Eigenfunctions for Polynomial Problems: Exact Results |
| title_fullStr | Infinitely Many Eigenfunctions for Polynomial Problems: Exact Results |
| title_full_unstemmed | Infinitely Many Eigenfunctions for Polynomial Problems: Exact Results |
| title_short | Infinitely Many Eigenfunctions for Polynomial Problems: Exact Results |
| title_sort | infinitely many eigenfunctions for polynomial problems exact results |
| url | http://dx.doi.org/10.1155/2015/516159 |
| work_keys_str_mv | AT yichouchen infinitelymanyeigenfunctionsforpolynomialproblemsexactresults |