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Stable manifolds for semi-linear evolution equations and admissibility of function spaces on a half-line. (English) Zbl 1170.34042
The author studies the existence of the stable manifold for some nonautonomous evolution equations in Banach spaces. The linear part is time dependent and has an exponential dichotomy. The nonlinear part is Lipschitz continuous and the Lipschitz coefficient is also time dependent. The Lipschitz coefficient function must be in admissible functions spaces which contain L p spaces. The results are interesting for applications and generalize some well known established results in the field when the Lipschitz coefficient is constant.
MSC:
34G20Nonlinear ODE in abstract spaces
34D09Dichotomy, trichotomy
34C30Manifolds of solutions of ODE (MSC2000)