On the oscillation and periodic character of a third order rational difference equation

DOI10.1090/S0002-9939-02-06611-XzbMath1014.39010MaRDI QIDQ4780430

William T. Patula, Hristo Dimitrov Voulov

Publication date: 19 November 2002

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

oscillationperiodic solutionpositive solutionsemicyclesthird order rational difference equation

Mathematics Subject Classification ID

Related Items (15)

On the Global Character of the Difference Equation X_{n+ 1}= ⋮ Short Note: A Note on Periodic Character of a Difference Equation ⋮ Dynamics of \(x_{n+1}=\frac{x_{n-2k+1}}{x_{n-22k+1}+\alpha x_{n-2l}}\) ⋮ Dynamics of Discrete Operator Equations ⋮ The periodic character of the difference equation \(x_{n+1}=f(x_{n - l+1},x_{n - 2k+1})\) ⋮ Some results about the global attractivity of bounded solutions of difference equations with applications to periodic solutions ⋮ On the recursive sequence \(x_{n+1}=A+x_{n}^{p}/x_{n-1}^{r}\) ⋮ Periodicity and boundedness for the integer solutions to a minimum-delay difference equation ⋮ The global attractivity of the rational difference equation 𝑦_{𝑛}=𝐴+(\frac{𝑦_{𝑛-𝑘}}𝑦_{𝑛-𝑚})^{𝑝} ⋮ Stability and periodic character of a rational third order difference equation ⋮ On the rational recursive sequence \(y_n = A + \frac{y_{n-1}}{y_{n-m}}\) for smalla ⋮ On the Dynamics of ⋮ Global asymptotic stability for minimum-delay difference equations ⋮ The global attractivity of the rational difference equation $y_{n}=1+\frac{y_{n-k}}{y_{n-m}}$ ⋮ The behaviour of the positive solutions of the difference equation

Cites Work

• Convergence of a difference equation via the full limiting sequences method
• On the global attractivity and the periodic character of some difference equations
• On the recursive sequence 𝑥_{𝑛+1}=\frac{𝐴}𝑥_{𝑛}+\frac{1}𝑥_{𝑛-2}
• Asymptotic 2–periodic difference equations with diagonally self–invertible responses
• Open Problems and Conjectures
• A global convergence result with applications to periodic solutions

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