Properties of Meromorphic Solutions of a Class of Second Order Linear Differential Equations

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Benharrat Belaidi, Habib Habib, Properties of Meromorphic Solutions of a Class of Second Order Linear Differential Equations, Int. J. Anal. Appl., 5 (2) (2014), 198-211.

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Benharrat Belaidi, Habib Habib

Abstract

This paper deals with the growth of meromorphic solutions of some second order linear differential equations, where it is assumed that the coefficients are meromorphic functions. Our results extend the previous results due to Chen and Shon, Xu and Zhang, Peng and Chen and others.

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References

  1. I. Amemiya and M. Ozawa, Non-existence of finite order solutions of w00 +e-zw0 +Q (z) w = 0, Hokkaido Math. J. 10 (1981), Special Issue, 1-17.
  2. B. Belaidi and H. Habib, On the growth of solutions of some second order linear differential equations with entire coefficients, An. S ¸t. Univ. Ovidius Constant ¸a, Vol. 21(2), (2013), 35-52.
  3. Z. X. Chen, The growth of solutions of f 00 + e-zf 0 + Q (z) f = 0 where the order (Q) = 1, Sci. China Ser. A 45 (2002), no. 3, 290-300. 4] Z. X. Chen and K. H. Shon, On the growth and fixed points of solutions of second order differential equations with meromorphic coefficients, Acta Math. Sin. (Engl. Ser.) 21 (2005), no. 4, 753-764.
  4. W. J. Chen and J. F. Xu, Growth order of meromorphic solutions of higher-order linear differential equations, Electron. J. Qual. Theory Differ. Equ., (2009), no. 1, 1-13.
  5. Y. M. Chiang and W. K. Hayman, Estimates on the growth of meromorphic solutions of linear differential equations, Comment. Math. Helv. 79 (2004), no. 3, 451-470.
  6. M. Frei, Uber die L ¨osungen linearer Differentialgleichungen mit ganzen Funktionen als Ko- ¨ effizienten, Comment. Math. Helv. 35 (1961), 201-222.
  7. M. Frei, Uber die Subnormalen L ¨osungen der Differentialgleichung ¨ w00 + e-zw0 + (Konst.) w = 0, Comment. Math. Helv. 36 (1961), 1-8.
  8. F. Gross, On the distribution of values of meromorphic functions, Trans. Amer. Math. Soc. 131(1968), 199-214.
  9. G. G. Gundersen, On the question of whether f 00 + e-zf 0 + B (z) f = 0 can admit a solution f 6≡ 0 of finite order, Proc. Roy. Soc. Edinburgh Sect. A 102 (1986), no. 1-2, 9-17.
  10. G. G. Gundersen, Estimates for the logarithmic derivative of a meromorphic function, plus similar estimates, J. London Math. Soc. (2) 37(1988), no. 1, 88-104.
  11. G. G. Gundersen, Finite order solutions of second order linear differential equations, Trans. Amer. Math. Soc. 305 (1988), no. 1, 415-429.
  12. W. K. Hayman, Meromorphic functions, Oxford Mathematical Monographs Clarendon Press, Oxford 1964.
  13. J. K. Langley, On complex oscillation and a problem of Ozawa, Kodai Math. J. 9 (1986), no. 3, 430-439.
  14. A. I. Markushevich, Theory of functions of a complex variable, Vol. II, translated by R. A. Silverman, Prentice-Hall, Englewood Cliffs, New Jersey, 1965.
  15. M. Ozawa, On a solution of w00 + e-zw0 + (az + b) w = 0, Kodai Math. J. 3 (1980), no. 2, 295-309.
  16. F. Peng and Z. X. Chen, On the growth of solutions of some second-order linear differential equations, J. Inequal. Appl. 2011, Art. ID 635604, 1-9.
  17. J. F. Xu and H. X. Yi, The relations between solutions of higher order differential equations with functions of small growth, Acta Math. Sinica, Chinese Series, 53 (2010), 291-296.
  18. J. F. Xu and X. B. Zhang, Some results of meromorphic solutions of second-order linear differential equations, J. Inequal. Appl. 2013, 2013:304, 14 pp.
  19. C. C. Yang and H. X. Yi, Uniqueness theory of meromorphic functions, Mathematics and its Applications, 557. Kluwer Academic Publishers Group, Dordrecht, 2003.