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Response Solutions for a Singularly Perturbed System Involving Reflection of the Argument

Author

Listed:
  • Shanliang Zhu
  • Shufang Zhang
  • Xinli Zhang
  • Qingling Li

Abstract

In this paper, the existence and uniqueness of response solutions, which has the same frequency ω with the nonlinear terms, are investigated for a quasiperiodic singularly perturbed system involving reflection of the argument. Firstly, we prove that all quasiperiodic functions with the frequency ω form a Banach space. Then, we obtain the existence and uniqueness of quasiperiodic solutions by means of the fixed‐point methods and the B‐property of quasiperiodic functions.

Suggested Citation

  • Shanliang Zhu & Shufang Zhang & Xinli Zhang & Qingling Li, 2020. "Response Solutions for a Singularly Perturbed System Involving Reflection of the Argument," Advances in Mathematical Physics, John Wiley & Sons, vol. 2020(1).
    • Handle: RePEc:wly:jnlamp:v:2020:y:2020:i:1:n:6738247
    DOI: 10.1155/2020/6738247
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    References listed on IDEAS

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    1. Chaitan P. Gupta, 1987. "Two-point boundary value problems involving reflection of the argument," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 10, pages 1-11, January.
    2. Joseph Wiener & A. R. Aftabizadeh, 1985. "Boundary value problems for differential equations with reflection of the argument," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 8, pages 1-13, January.
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