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

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. Google Scholar

  2. B. Bela¨ıdi, Oscillation of fast growing solutions of linear differential equations in the unit disc, Acta Univ. Sapientiae Math. 2 (2010), no. 1, 25–38. Google Scholar

  3. B. Bela¨ıdi, 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. Google Scholar

  4. B. Bela¨ıdi and Z. Latreuch, Relation between small functions with differential polynomials generated by meromorphic solutions of higher order linear differential equations, Submitted. Google Scholar

  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. Google Scholar

  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. Google Scholar

  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. Google Scholar

  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. Google Scholar

  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. Google Scholar

  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. Google Scholar

  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. Google Scholar

  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. Google Scholar

  13. A. El Farissi, B. Bela¨ıdi and Z. Latreuch, Growth and oscillation of differential polynomials in the unit disc, Electron. J. Diff. Equ., Vol. 2010(2010), No. 87, 1-7. Google Scholar

  14. W. K. Hayman, Meromorphic functions, Oxford Mathematical Monographs Clarendon Press, Oxford, 1964. Google Scholar

  15. J. Heittokangas, On complex differential equations in the unit disc, Ann. Acad. Sci. Fenn. Math. Diss. 122 (2000), 1-54. Google Scholar

  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. Google Scholar

  17. L. Kinnunen, Linear differential equations with solutions of finite iterated order, Southeast Asian Bull. Math. 22 (1998), no. 4, 385-405. Google Scholar

  18. I. Laine, Nevanlinna theory and complex differential equations, de Gruyter Studies in Mathematics, 15. Walter de Gruyter & Co., Berlin-New York, 1993. Google Scholar

  19. I. Laine and J. Rieppo, Differential polynomials generated by linear differential equations, Complex Var. Theory Appl. 49 (2004), no. 12, 897–911. Google Scholar

  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. Google Scholar

  21. Z. Latreuch and B. Bela¨ıdi, Growth and oscillation of differential polynomials generated by complex differential equations, Electron. J. Diff. Equ., Vol. 2013 (2013), No. 16, 1-14. Google Scholar

  22. M. Tsuji, Potential Theory in Modern Function Theory, Chelsea, New York, (1975), reprint of the 1959 edition. Google Scholar


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