Pacific Journal of Mathematics

Linear combinations of logarithmic derivatives of entire functions with applications to differential equations.

J. Miles and J. Rossi

Article information

Source
Pacific J. Math., Volume 174, Number 1 (1996), 195-214.

Dates
First available in Project Euclid: 6 December 2004

Permanent link to this document
https://projecteuclid.org/euclid.pjm/1102365365

Mathematical Reviews number (MathSciNet)
MR1398375

Zentralblatt MATH identifier
0861.30025

Subjects
Primary: 30D35: Distribution of values, Nevanlinna theory
Secondary: 34A20

Citation

Miles, J.; Rossi, J. Linear combinations of logarithmic derivatives of entire functions with applications to differential equations. Pacific J. Math. 174 (1996), no. 1, 195--214. https://projecteuclid.org/euclid.pjm/1102365365


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References

  • [1] S. Bank and I. Laine, On the oscillation theory of f" + Af = 0 where A is entire, Trans. Amer. Math. Soc, 273 (1982), 351-363.
  • [2] S. Bank and J. Langley, Oscillation theory of higher order linear differentialequa- tions with entire coefficients. Complex Variables, 16 (1991), 163-175.
  • [3] P. Barry, Some theorems related to the cosp theorem, Proc. London Math. Soc. (3), 21 (1970), 344-360.
  • [4] M. Cartwright, Integral Functions, Cambridge University Press, 1956.
  • [5] D. Drasin and D. Shea, Convolution inequalities, regular variation and exceptional sets, J. Analyse Math., 29 (1976), 232-293.
  • [6] W. Fuchs, Proof of a conjecture of G. Polya concerning gap series, 111. J. Math., 7 (1963), 661-667.
  • [7] W. Hayman, Meromorphic Functions, Oxford at the Clarendon Press, 1964.
  • [8] S. Hellerstein, J. Miles, and J. Rossi, On the growth of solutions of f"+gf+hf= 0, Trans. Amer. Math. Soc, 324 (1991), 693-706.
  • [9] S. Hellerstein, J. Miles, and J. Rossi, On the growth of solutions of certain linear differential equations, Ann. Acad. Sci. Fenn., 17 (1992), 343-365.
  • [10] J. Langley, Some oscillation theorems for higher order linear differential equations with entire coefficients of small growth, Results in Math., 20 (1991), 517-529.
  • [11] J. Rossi, Second order differential equations with transcendental coefficients, Proc. Amer. Math. Soc, 97 (1986), 61-66.
  • [12] L.-C. Shen, Solution to a problem of S. Bank regardingthe exponent of convergence of the solutions of a differential equation f" + Af --0, Kexue Tongbao, 30 (1985), 1581-1585.
  • [13] D. Townsend, Comparisons between T(r,f) and the total variation of arg f(re) and log \f(rei)\, J. Math. Anal, and Appl., 128 (1987), 347-361.