# zbMATH — the first resource for mathematics

Further results on common zeros of the solutions of two differential equations. (English) Zbl 1282.34092
Summary: Two problems are discussed. In the first problem, we consider one homogeneous and one non-homogeneous differential equation 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.
We apply the Nevanlinna theory and properties of entire solutions of linear differential equations.
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.
##### MSC:
 34M10 Oscillation, growth of solutions to ordinary differential equations in the complex domain 34M03 Linear ordinary differential equations and systems in the complex domain 30D35 Value distribution of meromorphic functions of one complex variable, Nevanlinna theory
##### Keywords:
Nevanlinna theory; differential equations
Full Text:
##### References:
 [1] doi:10.1090/S0002-9939-1986-0831388-8 · doi:10.1090/S0002-9939-1986-0831388-8 [2] doi:10.1186/1029-242X-2011-134 · Zbl 1276.34078 · doi:10.1186/1029-242X-2011-134 [3] doi:10.4153/CMB-1974-064-0 · Zbl 0314.30021 · doi:10.4153/CMB-1974-064-0
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.