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Common Zeros of the Solutions of Two Differential Equations

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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.

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References

  1. A. Alotaibi, On complex oscillation theory, Results in Mathematics 47 (2005), 165–175.

    MathSciNet  MATH  Google Scholar 

  2. 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.

    MathSciNet  MATH  Google Scholar 

  3. S. B. Bank and I. Laine, Representations of solutions of periodic second order linear differential equations, J. Reine Angew. Math. 344 (1983), 1–21.

    MathSciNet  MATH  Google Scholar 

  4. 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.

    MathSciNet  MATH  Google Scholar 

  5. 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.

    MathSciNet  MATH  Google Scholar 

  6. 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.

    Article  MathSciNet  MATH  Google Scholar 

  7. W. K. Hayman, Meromorphic Functions, Oxford Mathematical Monographs, Clarendon Press, Oxford, 1964.

    MATH  Google Scholar 

  8. 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.

    Article  MathSciNet  MATH  Google Scholar 

  9. E. Hille, Ordinary Differential Equations in the Complex Domain, Dover Publications Inc., Mineola, NY, 1997; Reprint of the 1976 original.

    MATH  Google Scholar 

  10. I. Laine, Nevanlinna Theory and Complex Differential Equations, de Gruyter Studies in Mathematics 15, Walter de Gruyter & Co., Berlin, 1993.

    Book  Google Scholar 

  11. 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.

    MathSciNet  MATH  Google Scholar 

  12. 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.

    MathSciNet  MATH  Google Scholar 

  13. J. Rossi, Second order differential equations with transcendental coefficients, Proc. Amer. Math. Soc. 97 (1986), 61–66.

    Article  MathSciNet  MATH  Google Scholar 

  14. H. Wittich, Neuere Untersuchungen über eindeutige analytische Funktionen, Ergebnisse der Mathematik und ihrer Grenzgebiete 8, Springer, Berlin, Göttingen, Heidelberg, 1955.

    MATH  Google Scholar 

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Correspondence to Asim Asiri.

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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

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