Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-29T03:57:17.428Z Has data issue: false hasContentIssue false
  • English
  • Français

Entire Solutions of

Published online by Cambridge University Press:  11 January 2016

Bao Qin li
Bao Qin li*
Affiliation:
Department of Mathematics, Florida International University, University Park, Miami, FL 33199, USA, libaoqin@fiu.edu
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The paper is concerned with description of entire solutions of the partial differential equations where m ≥ 2, n ≥ 2 are integers and g is a polynomial or an entire function in C2. Descriptions are given and complemented by various examples.

Keywords

35F2032A1532A22
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 178 , 2005 , pp. 151 - 162
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2005

References

[BG] Berenstein, C. A. and Gay, R., Complex Variables, Springer-Verlag, New York, 1991.Google Scholar
[Ca] Cartan, H., Sur les zeros des combinaisons linèaires de p functions holomorphes donnèes, Mathematica (Cluf), 7 (1933), 5–31.Google Scholar
[CH] Courant, R. and Hilbert, D., Methods of Mathematical Physics, Vol. II, partial differential equations, Interscience, New York, 1962.Google Scholar
[CLY] Chang, D. C., Li, B. Q. and Yang, C. C., On composition of meromorphic functions in several complex variables, Forum Math., 7 (1995), 77–94.Google Scholar
[G] Garabedian, P. R., Partial Differential Equations, New York, Wiley, 1964.Google Scholar
[GI] Iyer, V. Ganapathy, On certain functional equations, J. Indian Math. Soc., 3 (1939), 312–315.Google Scholar
[J] John, F., Partial Differential Equations, Springer-Verlag, New York, 1982.Google Scholar
[K] Khavinson, D., A note on entire solutions of the eiconal equation, A mer. Math. Mon., 102 (1995), 159–161.Google Scholar
[Kr] Krantz, S., Function Theory of Several Complex Variables, John Wiley & Sons, New York, 1982.Google Scholar
[Ma] Markushevich, J., Entire Functions, Amer. Elsevier Pub. Co., New York, 1966.Google Scholar
[Mo] Montel, P., Le¸cons sur les families normales de functions analytique et leurs applications, Gauthier-Villars, Paris, 1927.Google Scholar
[Sa] Saleeby, E. G., Entire and meromorphic solutions of Fermat type partial differential equations, Analysis, 19 (1999), 369–376.Google Scholar
[Sh] Shabat, B. V., Introduction to Complex Analysis, part II, Functions of several variables, Translation Mathematical Monographs, Vol. 110, American Mathematical Society, Providence, RI, 1992.Google Scholar
[St] Stoll, W., Introduction to the Value Distribution Theory of Meromorphic Functions, Springer-Verlag, New York, 1982.Google Scholar
[V] Vitter, A., The lemma of the logarithmic derivative in several complex variables, Duke Math. J., 44 (1977), 89–104.Google Scholar