Properties of Solutions of Complex Differential Equations in the Unit Disc

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Zinelaâbidine Latreuch, Benharrat BELAIDI, Properties of Solutions of Complex Differential Equations in the Unit Disc, Int. J. Anal. Appl., 4 (2) (2014), 159-173.

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Zinelaâbidine Latreuch, Benharrat BELAIDI

Abstract

In this paper, we investigate the growth and oscillation of higher order differential polynomial with meromorphic coefficients in the unit disc”¦

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References

  1. S. Bank, General theorem concerning the growth of solutions of first-order algebraic differential equations, Compositio Math. 25 (1972), 61-70.
  2. B. Bela ¨idi, Oscillation of fast growing solutions of linear differential equations in the unit disc, Acta Univ. Sapientiae Math. 2 (2010), no. 1, 25-38.
  3. B. Bela ¨idi, A. El Farissi, Fixed points and iterated order of differential polynomial generated by solutions of linear differential equations in the unit disc, J. Adv. Res. Pure Math. 3 (2011), no. 1, 161-172.
  4. B. Bela ¨idi and Z. Latreuch, Relation between small functions with differential polynomials generated by meromorphic solutions of higher order linear differential equations, Submitted.
  5. L. G. Bernal, On growth k-order of solutions of a complex homogeneous linear differential equation, Proc. Amer. Math. Soc. 101 (1987), no. 2, 317-322.
  6. T. B. Cao and H. X. Yi, The growth of solutions of linear differential equations with coeffi- cients of iterated order in the unit disc, J. Math. Anal. Appl. 319 (2006), no. 1, 278-294.
  7. T. B. Cao, The growth, oscillation and fixed points of solutions of complex linear differential equations in the unit disc, J. Math. Anal. Appl. 352 (2009), no. 2, 739-748.
  8. T. B. Cao, H. Y. Xu and C. X. Zhu, On the complex oscillation of differential polynomials generated by meromorphic solutions of differential equations in the unit disc, Proc. Indian Acad. Sci. Math. Sci. 120 (2010), no. 4, 481-493.
  9. T. B. Cao and Z. S. Deng, Solutions of non-homogeneous linear differential equations in the unit disc, Ann. Polo. Math. 97(2010), no. 1, 51-61.
  10. T. B. Cao, L. M. Li, J. Tu and H. Y. Xu, Complex oscillation of differential polynomials generated by analytic solutions of differential equations in the unit disc, Math. Commun. 16 (2011), no. 1, 205-214.
  11. Z. X. Chen and K. H. Shon, The growth of solutions of differential equations with coefficients of small growth in the disc, J. Math. Anal. Appl. 297 (2004), no. 1, 285-304.
  12. I. E. Chyzhykov, G. G. Gundersen and J. Heittokangas, Linear differential equations and logarithmic derivative estimates, Proc. London Math. Soc. (3) 86 (2003), no. 3, 735-754.
  13. A. El Farissi, B. Bela ¨idi and Z. Latreuch, Growth and oscillation of differential polynomials in the unit disc, Electron. J. Diff. Equ., Vol. 2010(2010), No. 87, 1-7.
  14. W. K. Hayman, Meromorphic functions, Oxford Mathematical Monographs Clarendon Press, Oxford, 1964.
  15. J. Heittokangas, On complex differential equations in the unit disc, Ann. Acad. Sci. Fenn. Math. Diss. 122 (2000), 1-54.
  16. J. Heittokangas, R. Korhonen and J. R ¨atty ¨a, Fast growing solutions of linear differential equations in the unit disc, Results Math. 49 (2006), no. 3-4, 265-278.
  17. L. Kinnunen, Linear differential equations with solutions of finite iterated order, Southeast Asian Bull. Math. 22 (1998), no. 4, 385-405.
  18. I. Laine, Nevanlinna theory and complex differential equations, de Gruyter Studies in Mathematics, 15. Walter de Gruyter & Co., Berlin-New York, 1993.
  19. I. Laine and J. Rieppo, Differential polynomials generated by linear differential equations, Complex Var. Theory Appl. 49 (2004), no. 12, 897-911.
  20. I. Laine, Complex differential equations, Handbook of differential equations: ordinary differential equations. Vol. IV, 269-363, Handb. Differ. Equ., Elsevier/North-Holland, Amsterdam, 2008.
  21. Z. Latreuch and B. Bela ¨idi, Growth and oscillation of differential polynomials generated by complex differential equations, Electron. J. Diff. Equ., Vol. 2013 (2013), No. 16, 1-14.
  22. M. Tsuji, Potential Theory in Modern Function Theory, Chelsea, New York, (1975), reprint of the 1959 edition.