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Further results on common zeros of the solutions of two differential equations

Asiri, Asim

Authors

Asim Asiri amkasiri@kau.edu.sa

Abstract

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.

Journal Article Type Article
Publication Date Oct 4, 2012
Journal Journal of Inequalities and Applications
Print ISSN 1025-5834
Electronic ISSN 1025-5834
Publisher Humana Press
Peer Reviewed Peer Reviewed
Volume 2012
Issue 222
Institution Citation Asiri, A. (2012). Further results on common zeros of the solutions of two differential equations. Journal of Inequalities and Applications, 2012(222), doi:10.1186/1029-242X-2012-222
DOI https://doi.org/10.1186/1029-242X-2012-222
Publisher URL http://www.journalofinequalitiesandapplications.com/content/2012/1/222
Copyright Statement Copyright information regarding this work can be found at the following address: http://creativecommons.org/licenses/by/4.0

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Copyright Statement
Copyright information regarding this work can be found at the following address: http://creativecommons.org/licenses/by/4.0




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