Exponential polynomials as solutions of certain nonlinear difference equations

DOI10.1007/S10114-012-1484-2zbMath1260.39027OpenAlexW1964425847MaRDI QIDQ1757956

Zhi-Tao Wen, Janne Heittokangas, Ilpo Laine

Publication date: 7 November 2012

Published in: Acta Mathematica Sinica. English Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10114-012-1484-2

zbMATH Keywords

Nevanlinna theoryconvex hullnonlinear difference equationentire solutionexponential polynomialmeromorphic solution

Mathematics Subject Classification ID

Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable (30D05) Value distribution of meromorphic functions of one complex variable, Nevanlinna theory (30D35) Meromorphic functions of one complex variable (general theory) (30D30) Special classes of entire functions of one complex variable and growth estimates (30D15) Difference equations in the complex domain (39A45)

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Good linear operators and meromorphic solutions of functional equations ⋮ Some results on transcendental entire solutions to certain nonlinear differential-difference equations ⋮ The properties of solutions of certain type of difference equations ⋮ Note on wandering domains in the dynamics of solutions of certain difference equations ⋮ 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 ⋮ Entire solutions of certain type of non-linear difference equations ⋮ On solutions of certain nonlinear delay-differential equations ⋮ Value distribution of exponential polynomials and their role in the theories of complex differential equations and oscillation theory ⋮ Unnamed Item ⋮ QUANTITATIVE PROPERTIES OF MEROMORPHIC SOLUTIONS TO SOME DIFFERENTIAL-DIFFERENCE EQUATIONS ⋮ Unnamed Item ⋮ A note on solutions of some differential-difference equations ⋮ Exponential polynomials as solutions of differential-difference equations of certain types ⋮ Some results of certain nonlinear delay differential equation ⋮ Entire solutions of two certain types of non-linear differential-difference equations ⋮ On the Fermat-type difference equation \(f^3(z)+[c_1f(z+c)+c_0f(z)^3=E^{\alpha z+\beta}\)] ⋮ Entire solutions of some differential-difference equations ⋮ Exponential polynomials and nonlinear differential-difference equations ⋮ On entire solutions of some type of nonlinear difference equations ⋮ Entire solutions of one certain type of nonlinear differential-difference equations ⋮ 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

• Unnamed Item
• On the Nevanlinna characteristic of \(f(z+\eta)\) and difference equations in the complex plane
• On analogies between nonlinear difference and differential equations
• Nevanlinna theory and complex differential equations
• Zur Wertverteilung von Exponentialpolynomen
• On entire solutions of a certain type of nonlinear differential equation
• On meromorphic solutions of certain nonlinear differential equations

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