Abstract
In this article, we give the existence of a smooth stable manifold which is invariant under the semiflows of the delay differential equation \( x^{\prime }= Ax(t) + Lx_t + f(t,x_t, \lambda ) \), with the assumption that the corresponding linear differential equation admits a nonuniform exponential dichotomy and the perturbation f(t, xt, λ) is small and smooth enough. We also show that the obtained manifold is Lipschitz in the parameter λ.
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The authors would like to thank the referees for their valuable comments and suggestions for considerably improving the original manuscript.
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Singh, L., Bahuguna, D. Smooth Invariant Manifolds for Differential Equations with Infinite Delay. J Dyn Control Syst 27, 107–132 (2021). https://doi.org/10.1007/s10883-020-09498-y
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DOI: https://doi.org/10.1007/s10883-020-09498-y
Keywords
- Functional differential equation
- Nonuniform exponential dichotomy
- Invariant manifold theory
- Parameter dependence