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A remark on k th-order linear functional equations with constant coefficients

Abstract

Abel functional equations are associated to a linear homogeneous functional equation with constant coefficients. The work uses the space S of continuous strictly monotonic functions. Generalized terms are used, because of the space S, like composite function, iterates of a function, Abel functional equation, and linear homogeneous functional equation in S with constant coefficients. The classical theory of linear homogeneous functional and difference equations is obtained as a special case of the theory in space S. Equivalence of points and orbits of a point are introduced to show the connection between the linear functional and the linear difference equations in S. Asymptotic behavior at infinity is studied for a solution of the linear functional equation.

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Correspondence to Jitka Laitochová.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Laitochová, J. A remark on k th-order linear functional equations with constant coefficients. Adv Differ Equ 2006, 072615 (2006). https://doi.org/10.1155/ADE/2006/72615

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Keywords

  • Differential Equation
  • Partial Differential Equation
  • Ordinary Differential Equation
  • Functional Analysis
  • Asymptotic Behavior