Abstract
The influence of the normality of the coefficient
Open Access
Interaction between coefficient conditions and solution conditions of differential equations in the unit disk
Received17 Sept 2005
Revised07 Jun 2006
Accepted22 Jun 2006
Published01 Oct 2006
References
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 Site | Google Scholar | Zentralblatt MATH | MathSciNetF. 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 | Zentralblatt MATH | MathSciNetD. Benbourenane, Value distribution for solutions of complex differential equations in the unit disk, M.S. thesis, Northern Illinois University, Illinois, 2001.
View at: Google ScholarD. 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 | MathSciNetZ.-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 Site | Google Scholar | Zentralblatt MATH | MathSciNetK. E. Fowler, Normal functions, the MacLane class, and complex differential equations in the unit disk, M.S. thesis, Northern Illinois University, Illinois, 2004.
View at: Google ScholarW. K. Hayman and D. A. Storvick, “On normal functions,” The Bulletin of the London Mathematical Society, vol. 3, pp. 193–194, 1971.
View at: Google Scholar | Zentralblatt MATH | MathSciNetJ. Heittokangas, “On complex differential equations in the unit disc,” Annales Academiae Scientiarum Fennicae. Mathematica. Dissertationes, no. 122, p. 54, 2000.
View at: Google Scholar | Zentralblatt MATH | MathSciNetP. 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 | Zentralblatt MATH | MathSciNetO. 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 Site | Google Scholar | Zentralblatt MATH | MathSciNetK. 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 | Zentralblatt MATHC. 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 | Zentralblatt MATH | MathSciNetJ. L. Schiff, Normal Families, Universitext, Springer, New York, 1993.
View at: Google Scholar | Zentralblatt MATH | MathSciNetD. 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 | Zentralblatt MATH | MathSciNetH. Wulan, “On some classes of meromorphic functions,” Annales Academiae Scientiarum Fennicae. Mathematica. Dissertationes, no. 116, pp. 1–57, 1998.
View at: Google Scholar | Zentralblatt MATH | MathSciNetY. Xu, “The -normal functions,” Computers & Mathematics with Applications, vol. 44, no. 3-4, pp. 357–363, 2002.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetK. 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 | Zentralblatt MATH | MathSciNet
Copyright
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.