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International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 52583, 11 pages
http://dx.doi.org/10.1155/IJMMS/2006/52583

Interaction between coefficient conditions and solution conditions of differential equations in the unit disk

1Department of Mathematics, University of Tampa, Tampa 33606, FL, USA
2Department of Mathematical Sciences, Northern Illinois University, DeKalb 60115, IL, USA

Received 17 September 2005; Revised 7 June 2006; Accepted 22 June 2006

Copyright © 2006 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. R. Aulaskari and P. Lappan, “An integral criterion for normal functions,” Proceedings of the American Mathematical Society, vol. 103, no. 2, pp. 438–440, 1988. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. F. Bagemihl and W. Seidel, “Sequential and continuous limits of meromorphic functions,” Annales Academiae Scientiarum Fennicae. Series A I. Mathematica, vol. 280, pp. 1–17, 1960. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. D. Benbourenane, Value distribution for solutions of complex differential equations in the unit disk, M.S. thesis, Northern Illinois University, Illinois, 2001.
  4. D. Benbourenane and L. R. Sons, “On global solutions of complex differential equations in the unit disk,” Complex Variables Theory and Application, vol. 49, no. 13, pp. 913–925, 2004. View at Google Scholar · View at MathSciNet
  5. Z.-X. Chen and K. H. Shon, “The growth of solutions of differential equations with coefficients of small growth in the disc,” Journal of Mathematical Analysis and Applications, vol. 297, no. 1, pp. 285–304, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. K. E. Fowler, Normal functions, the MacLane class, and complex differential equations in the unit disk, M.S. thesis, Northern Illinois University, Illinois, 2004.
  7. W. K. Hayman and D. A. Storvick, “On normal functions,” The Bulletin of the London Mathematical Society, vol. 3, pp. 193–194, 1971. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. J. Heittokangas, “On complex differential equations in the unit disc,” Annales Academiae Scientiarum Fennicae. Mathematica. Dissertationes, no. 122, p. 54, 2000. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. P. Lappan, “The spherical derivative and normal functions,” Annales Academiae Scientiarum Fennicae. Series A I. Mathematica, vol. 3, no. 2, pp. 301–310, 1977. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. O. Lehto and K. I. Virtanen, “Boundary behaviour and normal meromorphic functions,” Acta Mathematica, vol. 97, no. 1–4, pp. 47–65, 1957. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. K. Noshiro, “Contributions to the theory of meromorphic functions in the unit-circle,” Journal of the Faculty of Science, Hokkaido University, vol. 7, pp. 149–159, 1938. View at Google Scholar · View at Zentralblatt MATH
  12. C. Pommerenke, “On the mean growth of the solutions of complex linear differential equations in the disk,” Complex Variables Theory and Application, vol. 1, no. 1, pp. 23–38, 1982/1983. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. J. L. Schiff, Normal Families, Universitext, Springer, New York, 1993. View at Zentralblatt MATH · View at MathSciNet
  14. D. F. Shea and L. R. Sons, “Value distribution theory for meromorphic functions of slow growth in the disk,” Houston Journal of Mathematics, vol. 12, no. 2, pp. 249–266, 1986. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. H. Wulan, “On some classes of meromorphic functions,” Annales Academiae Scientiarum Fennicae. Mathematica. Dissertationes, no. 116, pp. 1–57, 1998. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. Y. Xu, “The α-normal functions,” Computers & Mathematics with Applications, vol. 44, no. 3-4, pp. 357–363, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. K. H. Zhu, “Bloch type spaces of analytic functions,” The Rocky Mountain Journal of Mathematics, vol. 23, no. 3, pp. 1143–1177, 1993. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet