Open Access Research

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

Asim Asiri

Author Affiliations

Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah, 21589, Saudi Arabia

Journal of Inequalities and Applications 2012, 2012:222  doi:10.1186/1029-242X-2012-222

Published: 4 October 2012

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.

Keywords:
Nevanlinna theory; differential equations