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Existence and Uniqueness of Solution for Perturbed Nonautonomous Systems with Nonuniform Exponential Dichotomy

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  • Yong-Hui Xia
  • Xiaoqing Yuan
  • Kit Ian Kou
  • Patricia J. Y. Wong

Abstract

Nonuniform exponential dichotomy has been investigated extensively. The essential condition of these previous results is based on the assumption that the nonlinear term satisfies . However, this condition is very restricted. There are few functions satisfying . In some sense, this assumption is not reasonable enough. More suitable assumption should be . To the best of the authors' knowledge, there is no paper considering the existence and uniqueness of solution to the perturbed nonautonomous system with a relatively conservative assumption . In this paper, we prove that if the nonlinear term is bounded, the perturbed nonautonomous system with nonuniform exponential dichotomy has a unique solution. The technique employed to prove Theorem 4 is the highlight of this paper.

Suggested Citation

  • Yong-Hui Xia & Xiaoqing Yuan & Kit Ian Kou & Patricia J. Y. Wong, 2014. "Existence and Uniqueness of Solution for Perturbed Nonautonomous Systems with Nonuniform Exponential Dichotomy," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-10, May.
    • Handle: RePEc:hin:jnlaaa:725098
    DOI: 10.1155/2014/725098
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