On difference equations with powers as solutions and their connection with invariant curves

DOI10.1016/j.amc.2011.02.005zbMath1260.39002OpenAlexW2031279370MaRDI QIDQ531636

Stevo Stević, Lothar Berg

Publication date: 19 April 2011

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2011.02.005

zbMATH Keywords

system of nonlinear difference equationsequation of invariant curvespower functions as solutionsself-reversed polynomials

Mathematics Subject Classification ID

Additive difference equations (39A10)

Related Items (20)

More on a rational second-order difference equation ⋮ On some solvable difference equations and systems of difference equations ⋮ Unique existence of bounded continuous solutions on the real line of a class of nonlinear functional equations with complicated deviations ⋮ On the difference equation \(x_{n}=x_{n-k} / (b+cx_{n-q}+\dots{ }+x_{n-k})\) ⋮ On some solvable systems of difference equations ⋮ On the difference equation \(x_{n} = x_{n - 2}/(b_{n} + c_{n}x_{n - 1}x_{n - 2})\) ⋮ On a third-order system of difference equations ⋮ On a third-order system of difference equations with variable coefficients ⋮ Solutions of a max-type system of difference equations ⋮ On some linear difference equations and inequalities with continuous argument ⋮ On the difference equation \(x_{n+1} = x_nx_{n-k}/(x_{n-k+1}(a + bx_nx_{n-k}))\) ⋮ On continuous solutions of a class of systems of nonlinear functional difference equations with deviating argument ⋮ Local existence of Lipschitz-continuous solutions of systems of nonlinear functional equations with iterated deviations ⋮ On some systems of difference equations ⋮ On a solvable system of difference equations of \(k\)th order ⋮ On a system of difference equations of odd order solvable in closed form ⋮ Difference equations and nonexistence of solutions of an integral equation ⋮ Domains of undefinable solutions of some equations and systems of difference equations ⋮ On a solvable system of rational difference equations ⋮ On a class of solvable higher-order difference equations

Cites Work

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• Global stability and asymptotics of some classes of rational difference equations
• On the asymptotics of nonlinear difference equations
• On the recursive sequence \(x_{n+1}=x_{n-1}/g(x_n)\)
• Convergence of solutions in a nonhyperbolic case.
• Existence of nontrivial solutions of a rational difference equation
• Asymptotics of some classes of higher-order difference equations
• On positive solutions of a (\(k+1\))th order difference equation
• On a class of composite functional equations in a single variable
• On the asymptotics of the difference equation
• Recent results on functional equations in a single variable, perspectives and open problems
• Eigenfunctions of two-scale difference equations and Appell polynomials

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