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An Equivalent Form of Picard's Theorem and Beyond

  • Bao Qin Li,
    Department of Mathematics and Statistics, Florida International University, Miami, FL 33199 USA
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Abstract

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.
Keywords: entire function, Picard's Theorem, functional equation, partial differential equation entire function, Picard's Theorem, functional equation, partial differential equation
MSC Classifications: 30D20, 32A15, 35F20 show english descriptions Entire functions, general theory
Entire functions
Nonlinear first-order equations
30D20 - Entire functions, general theory
32A15 - Entire functions
35F20 - Nonlinear first-order equations
 

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