Further results on common zeros of the solutions of two differential equations
Purpose: Two problems are discussed in this paper. In the first problem, we consider one homogeneous and one non-homogeneous differential equations and study when the solutions of these differential equations can have (nearly) the same zeros. In the second problem, we consider two linear second-orde...
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| Format: | Article |
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SpringerOpen
2012
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| Online Access: | https://eprints.nottingham.ac.uk/3007/ |
| _version_ | 1848790930040029184 |
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| author | Asiri, Asim |
| author_facet | Asiri, Asim |
| author_sort | Asiri, Asim |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | Purpose: Two problems are discussed in this paper. In the first problem, we consider one homogeneous and one non-homogeneous differential equations and study when the solutions of these differential equations can have (nearly) the same zeros. In the second problem, we consider two linear second-order differential equations and investigate when the solutions of these differential equations can take the value 0 and a non-zero value at (nearly) the same points.
Method: We apply the Nevanlinna theory and properties of entire solutions of linear differential equations.
Conclusion: In the first problem, the results determine all pairs of such equations having solutions with the same zeros or nearly the same zeros. Regarding the second problem, the results also show all pairs of such equations having solutions taking the value 0 and a non-zero value at (nearly) the same points. |
| first_indexed | 2025-11-14T18:20:26Z |
| format | Article |
| id | nottingham-3007 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T18:20:26Z |
| publishDate | 2012 |
| publisher | SpringerOpen |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-30072020-05-04T16:34:34Z https://eprints.nottingham.ac.uk/3007/ Further results on common zeros of the solutions of two differential equations Asiri, Asim Purpose: Two problems are discussed in this paper. In the first problem, we consider one homogeneous and one non-homogeneous differential equations and study when the solutions of these differential equations can have (nearly) the same zeros. In the second problem, we consider two linear second-order differential equations and investigate when the solutions of these differential equations can take the value 0 and a non-zero value at (nearly) the same points. Method: We apply the Nevanlinna theory and properties of entire solutions of linear differential equations. Conclusion: In the first problem, the results determine all pairs of such equations having solutions with the same zeros or nearly the same zeros. Regarding the second problem, the results also show all pairs of such equations having solutions taking the value 0 and a non-zero value at (nearly) the same points. SpringerOpen 2012-10-04 Article PeerReviewed Asiri, Asim (2012) Further results on common zeros of the solutions of two differential equations. Journal of Inequalities and Applications, 2012 (222). ISSN 1025-5834 http://www.journalofinequalitiesandapplications.com/content/2012/1/222 doi:10.1186/1029-242X-2012-222 doi:10.1186/1029-242X-2012-222 |
| spellingShingle | Asiri, Asim Further results on common zeros of the solutions of two differential equations |
| title | Further results on common zeros of the solutions of two differential equations |
| title_full | Further results on common zeros of the solutions of two differential equations |
| title_fullStr | Further results on common zeros of the solutions of two differential equations |
| title_full_unstemmed | Further results on common zeros of the solutions of two differential equations |
| title_short | Further results on common zeros of the solutions of two differential equations |
| title_sort | further results on common zeros of the solutions of two differential equations |
| url | https://eprints.nottingham.ac.uk/3007/ https://eprints.nottingham.ac.uk/3007/ https://eprints.nottingham.ac.uk/3007/ |