Value distribution of the Painlevé transcendents

DOI10.1007/BF02785417zbMath1016.34091OpenAlexW2137950485MaRDI QIDQ701352

Norbert Steinmetz

Publication date: 23 October 2002

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02785417

zbMATH Keywords

Painlevé transcendentsorder of growthspherical derivativeNevanlinna characteristic function

Mathematics Subject Classification ID

Value distribution of meromorphic functions of one complex variable, Nevanlinna theory (30D35) Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) Oscillation, growth of solutions to ordinary differential equations in the complex domain (34M10)

Related Items (14)

Airy solutions of Painlevé's second equation ⋮ Poles and \(\alpha\)-points of meromorphic solutions of the first Painlevé hierarchy ⋮ On meromorphic solutions of certain nonlinear differential equations ⋮ Estimates of the proximate function of differential polynomials ⋮ Equi-Distribution of Values for the Third and the Fifth Painlevé Transcendents ⋮ The Yosida class is universal ⋮ Special polynomials associated with rational solutions of the Painlevé equations and applications to soliton equations ⋮ On shared-value properties of Painlevé transcendents ⋮ Value Distribution and Growth of Solutions of Certain Painlevé Equations ⋮ Transcendental Meromorphic Solutions of P 34 and Small Targets ⋮ Remarks on Painlevé's differential equation \(P_{34}\) ⋮ Meromorphic solutions of P_4,34 and their value distribution ⋮ An old new class of meromorphic functions ⋮ Painlevé σ-equations S1, S2, S4 and their value distribution

Cites Work

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• Zur Wertverteilung der Lösungen der vierten Painleveschen Differentialgleichung
• On normal criterion of meromorphic functions
• Bloch's principle and normal criterion
• Eindeutige Lösungen der Differentialgleichungen \(w=P(z,w)\)
• On the Growth of Logarithmic Derivatives
• A Heuristic Principle in Complex Function Theory
• On Painlevé's equations I, II and IV
• Solutions of the first and second Painlevé equations are meromorphic

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