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Zbl 1170.34042
Nguyen, Thieu Huy
Stable manifolds for semi-linear evolution equations and admissibility of function spaces on a half-line. (English)
[J] J. Math. Anal. Appl. 354, No. 1, 372-386 (2009). ISSN 0022-247X

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.
[Khalil Ezzinbi (Marrakech)]

MSC 2000:: *34G20 Nonlinear ODE in abstract spaces
34D09 Dichotomy, trichotomy
34C30 Manifolds of solutions of ODE

Keywords: semi linear evolution equation; integral equation; exponential dichotomy; local stable manifold; invariant stable manifold

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