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(Q, T)‐affine‐periodic solutions and Pseudo (Q, T)‐affine‐periodic solutions for Dynamic Equations on Time Scales

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  • Ruichao Guo
  • Xiaomeng Jiang
  • Hongren Wang

Abstract

The aim of this paper is to study the existence of (Q, T)‐affine‐periodic solutions for affine‐periodic systems on time scales of the type xΔ(t) = A(t)x(t) + f(t) and xΔt=Atxt+gt,xt,t∈T, assuming that corresponding homogeneous equation of this system admits exponential dichotomy. The result is also extended to the case of pseudo (Q, T)‐affine‐periodic solutions. The main approaches are based on the Banach contraction mapping principle, but certain technical aspects on time scales are more complicated.

Suggested Citation

  • Ruichao Guo & Xiaomeng Jiang & Hongren Wang, 2022. "(Q, T)‐affine‐periodic solutions and Pseudo (Q, T)‐affine‐periodic solutions for Dynamic Equations on Time Scales," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:jjmath:v:2022:y:2022:i:1:n:6874460
    DOI: 10.1155/2022/6874460
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    References listed on IDEAS

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    1. Damiano Brigo & Fabio Mercurio, 2000. "Option pricing impact of alternative continuous-time dynamics for discretely-observed stock prices," Finance and Stochastics, Springer, vol. 4(2), pages 147-159.
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