Orders of solutions of an n-th order linear differential equation with entire coefficients
We study the solutions of the differential equation $$ f^{(n)}+A_{n-1}(z) f^{(n-1) }+dots+A_{1}(z)f'+A_{0}(z) f=0, $$ where the coefficients are entire functions. We find conditions on the coefficients so that every solution that is not identically zero has infinite order.
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2001-09-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2001/61/abstr.html |
| _version_ | 1818750891593826304 |
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| author | Benharrat Belaidi Saada Hamouda |
| author_facet | Benharrat Belaidi Saada Hamouda |
| author_sort | Benharrat Belaidi |
| collection | DOAJ |
| description | We study the solutions of the differential equation $$ f^{(n)}+A_{n-1}(z) f^{(n-1) }+dots+A_{1}(z)f'+A_{0}(z) f=0, $$ where the coefficients are entire functions. We find conditions on the coefficients so that every solution that is not identically zero has infinite order. |
| first_indexed | 2024-12-18T04:26:53Z |
| format | Article |
| id | doaj.art-3291fe8007b4471bb3a3f78ba913139d |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-12-18T04:26:53Z |
| publishDate | 2001-09-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-3291fe8007b4471bb3a3f78ba913139d2022-12-21T21:21:05ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912001-09-0120016115Orders of solutions of an n-th order linear differential equation with entire coefficientsBenharrat BelaidiSaada HamoudaWe study the solutions of the differential equation $$ f^{(n)}+A_{n-1}(z) f^{(n-1) }+dots+A_{1}(z)f'+A_{0}(z) f=0, $$ where the coefficients are entire functions. We find conditions on the coefficients so that every solution that is not identically zero has infinite order.http://ejde.math.txstate.edu/Volumes/2001/61/abstr.htmlLinear differential equationsentire functionsorder of growth. |
| spellingShingle | Benharrat Belaidi Saada Hamouda Orders of solutions of an n-th order linear differential equation with entire coefficients Electronic Journal of Differential Equations Linear differential equations entire functions order of growth. |
| title | Orders of solutions of an n-th order linear differential equation with entire coefficients |
| title_full | Orders of solutions of an n-th order linear differential equation with entire coefficients |
| title_fullStr | Orders of solutions of an n-th order linear differential equation with entire coefficients |
| title_full_unstemmed | Orders of solutions of an n-th order linear differential equation with entire coefficients |
| title_short | Orders of solutions of an n-th order linear differential equation with entire coefficients |
| title_sort | orders of solutions of an n th order linear differential equation with entire coefficients |
| topic | Linear differential equations entire functions order of growth. |
| url | http://ejde.math.txstate.edu/Volumes/2001/61/abstr.html |
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