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

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

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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.

Item Type: Article
Schools/Departments: University of Nottingham UK Campus > Faculty of Science > School of Mathematical Sciences
Identification Number: https://doi.org/10.1186/1029-242X-2012-222
Depositing User: Johnson, Mrs Alison
Date Deposited: 25 Apr 2014 10:11
Last Modified: 14 Sep 2016 14:30
URI: http://eprints.nottingham.ac.uk/id/eprint/3007

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