An extension of Picard's theorem for meromorphic functions of small hyper-order

DOI10.1016/J.JMAA.2009.04.011zbMath1173.30017arXiv0903.3872OpenAlexW2013247730MaRDI QIDQ1025835

Risto Korhonen

Publication date: 23 June 2009

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0903.3872

zbMATH Keywords

value distributionsecond main theoremPicard's theoremhyper-orderforward invariant

Mathematics Subject Classification ID

Value distribution of meromorphic functions of one complex variable, Nevanlinna theory (30D35)

Related Items (11)

Good linear operators and meromorphic solutions of functional equations ⋮ Some results on transcendental entire solutions to certain nonlinear differential-difference equations ⋮ Normal families and growth of meromorphic functions with their \(k\)th derivatives ⋮ Growth of meromorphic function sharing functions and some uniqueness problems ⋮ Solutions of nonlinear difference equations ⋮ Exponential polynomials as solutions of nonlinear differential-difference equations ⋮ Characterization of exponential polynomial as solution of certain type of nonlinear delay-differential equation ⋮ On meromorphic solutions of the Fermat-type functional equations \(f(z)^3 + f(z+c)^3 = e^p\) ⋮ Some results of certain nonlinear delay differential equation ⋮ Some results on the transcendental entire solutions of certain type of non-linear shift-differential equations ⋮ Meromorphic solutions of certain nonlinear difference equations

Cites Work

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• On the Nevanlinna characteristic of \(f(z+\eta)\) and difference equations in the complex plane
• Painlevé differential equations in the complex plane
• Difference analogue of the lemma on the logarithmic derivative with applications to difference equations
• Holomorphic curves with shift-invariant hyperplane preimages
• Finite-order meromorphic solutions and the discrete Painlevé equations
• Nevanlinna theory for the $q$-difference operator and meromorphic solutions of $q$-difference equations

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