Abstract
We consider two homogeneous linear differential equations and use Nevanlinna theory to determine when the solutions of these differential equations can have the same zeros or nearly the same zeros.
Similar content being viewed by others
References
A. Alotaibi, On complex oscillation theory, Results in Mathematics 47 (2005), 165–175.
S. B. Bank and I. Laine, On the oscillation theory of f″ + Af = 0 where A is entire, Trans. Amer. Math. Soc. 273 no.1 (1982), 351–363.
S. B. Bank and I. Laine, Representations of solutions of periodic second order linear differential equations, J. Reine Angew. Math. 344 (1983), 1–21.
S. B. Bank, I. Laine and J. K. Langley, On the frequency of zeros of solutions of second order linear differential equations, Results Math. 10 (1986), 8–24.
S. B. Bank, I. Laine and J. K. Langley, Oscillation results for solutions of linear differential equations in the complex plane, Results Math. 16 (1989), 3–15.
S. B. Bank and J. K. Langley, Oscillation theory for higher order linear differential equations with entire coefficients, Complex Variables Theory Appl. 16 no.2–3 (1991), 163–175.
W. K. Hayman, Meromorphic Functions, Oxford Mathematical Monographs, Clarendon Press, Oxford, 1964.
W. K. Hayman, The local growth of power series: a survey of the Wiman-Valiron method, Canad. Math. Bull 17 no.3 (1974), 317–358.
E. Hille, Ordinary Differential Equations in the Complex Domain, Dover Publications Inc., Mineola, NY, 1997; Reprint of the 1976 original.
I. Laine, Nevanlinna Theory and Complex Differential Equations, de Gruyter Studies in Mathematics 15, Walter de Gruyter & Co., Berlin, 1993.
J. K. Langley, Some oscillation theorems for higher order linear differential equations with entire coefficients of small growth, Results Math. 20 no.1–2 (1991), 517–529.
J. K. Langley, On entire solutions of linear differential equations with one dominant coefficient, Analysis 15 no.2 (1995), 187–204; Corrections: Analysis 15 (1995), 433.
J. Rossi, Second order differential equations with transcendental coefficients, Proc. Amer. Math. Soc. 97 (1986), 61–66.
H. Wittich, Neuere Untersuchungen über eindeutige analytische Funktionen, Ergebnisse der Mathematik und ihrer Grenzgebiete 8, Springer, Berlin, Göttingen, Heidelberg, 1955.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Asiri, A. Common Zeros of the Solutions of Two Differential Equations. Comput. Methods Funct. Theory 12, 67–85 (2012). https://doi.org/10.1007/BF03321813
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF03321813