Geodesic
An Equivalent Form of Picard’s Theorem and Beyond
Canadian mathematical bulletin, Tome 61 (2018) no. 1, pp. 142-148

Voir la notice de l'article provenant de la source Cambridge University Press

This paper gives an equivalent form of Picard’s theorem via entire solutions of the functional equation ${{f}^{2}}\,+\,{{g}^{2}}\,=\,1$ and then its improvements and applications to certain nonlinear (ordinary and partial) differential equations.
DOI : 10.4153/CMB-2017-010-x
Mots-clés : 30D20, 32A15, 35F20, entire function, Picard’s Theorem, functional equation, partial differential equation 
Li, Bao Qin. An Equivalent Form of Picard’s Theorem and Beyond. Canadian mathematical bulletin, Tome 61 (2018) no. 1, pp. 142-148. doi: 10.4153/CMB-2017-010-x
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[I] [I] Ahlfors, L. V., Conformal invariants: topics in geometrical function theory. McGraw-Hill Series in Higher Mathematics, McGraw-Hill, New York, 1973. Google Scholar

[2] [2] Borel, E., Sur les zeros desfunctions entieres. Acta Math. 20 (1897), no. 1, 357–396. http://dx.doi.Org/10.1007/BF02418037. Google Scholar

[3] [3] Courant, R. and Hubert, D., Methods of mathematicalphysics, II. Partial differential equations. Wiley Classics Library, John Wiley & Sons, 1991. Google Scholar

[4] [4] Davis, B., Picard's theorem and Brownian motion. Trans. Amer. Math. Soc. 23 (1975), 353–362. http://dx.doi.Org/10.2307/1998050. Google Scholar

[5] [5] Fuchs, W. H. J., Topics in the theory offunctions ofone complex variable. D. Van Nostrand, Princeton, NJ, 1967. Google Scholar

[6] [6] Hayman, W. K., Meromorphic functions. Clarendon Press, Oxford, 1964. Google Scholar

[7] [7] Hille, E., Ordinary differential equations in the complex domain. Dover, Mineola, NY, 1997. Google Scholar

[8] [8] Lewis, J. L., Picard's theorem and Richman's theorem by way ofHarnack's inequality. Proc. Amer. Math. Soc. 122 (1994), 199–206. http://dx.doi.org/10.2307/2160861. Google Scholar

[9] [9] Li, B. Q., On meromorphic Solutions off2 + g2 = 1. Math. Z. 258 (2008), 763–771. http://dx.doi.Org/10.1007/s00209-007-01 96-2. Google Scholar

[10] [10] Li, B. Q., On Fermat-type functional and partial differential equations. Springer Proceedings in Mathematics, 16, Springer, Milan, 2012, pp. 209–222. http://dx.doi.org/10.1007/978-88-470-1947-8J3 Google Scholar

[11] [11] Li, B. Q., Estimates on derivatives and logarithmic derivatives of holomorphic functions and Picard's theorem. J. Math. Anal. Appl. 442 (2016), no. 2, 446–450. http://dx.doi.Org/10.1016/j.jmaa.2O16.04.060. Google Scholar

[12] [12] Saleeby, E. G., Meromorphic Solutions of generalized inviscid Burgers’ equations and afamily of quadratic PDEs. J. Math. Anal. Appl. 425 (2015), 508–519. http://dx.doi.Org/10.1016/j.jmaa.2O14.12.046. Google Scholar

[13] [13] Zhang, G. Y., Curves, domains and Picard's theorem. Bull. London Math. Soc. 34 (2002), 205–211. http://dx.doi.Org/10.1112/SOO24609301008712 Google Scholar

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