On difference Riccati equations and second order linear difference equations

DOI10.1007/s00010-010-0060-zzbMath1215.39021OpenAlexW2041467983MaRDI QIDQ633256

Katsuya Ishizaki

Publication date: 31 March 2011

Published in: Aequationes Mathematicae (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00010-010-0060-z

zbMATH Keywords

linear difference equationsmeromorphic solutionsmeromorphic functionsdifference Riccati equations

Mathematics Subject Classification ID

Difference equations, scaling ((q)-differences) (39A13) Special classes of entire functions of one complex variable and growth estimates (30D15) Linear difference equations (39A06) Difference equations in the complex domain (39A45)

Related Items (14)

On existence of solutions of difference Riccati equation ⋮ On fixed points of meromorphic functions \(f(z)\) and \(f(z + c)\), \(\delta_c f(z)\) ⋮ Fixed points of meromorphic functions and of their differences, divided differences and shifts ⋮ On \(q\)-difference Riccati equations and second-order linear \(q\)-difference equations ⋮ Meromorphic solutions of linear difference equations with polynomial coefficients ⋮ On growth of meromorphic solutions for linear difference equations with meromorphic coefficients ⋮ Some properties of algebraic difference equations of first order ⋮ THE VALUE DISTRIBUTION OF MEROMORPHIC SOLUTIONS OF SOME SECOND ORDER NONLINEAR DIFFERENCE EQUATION ⋮ Binomial series and complex difference equations ⋮ Zeros and fixed-points on meromorphic solutions of a certain type of first order difference equation ⋮ Complex oscillation of meromorphic solutions for difference Riccati equation ⋮ On growth of meromorphic solutions for linear difference equations ⋮ Meromorphic solutions of difference Riccati equations ⋮ Unnamed Item

Cites Work

• On the zeros of meromorphic solutions of second-order linear differential equations
• On the Nevanlinna characteristic of \(f(z+\eta)\) and difference equations in the complex plane
• Nevanlinna theory and complex differential equations
• The Nevanlinna functions of the Riemann zeta-function
• Difference analogue of the lemma on the logarithmic derivative with applications to difference equations
• Meromorphic solutions of the Riccati differential equation
• Wiman-Valiron method for difference equations
• Clunie theorems for difference and q -difference polynomials
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