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Zbl 1178.34070
Huy, Nguyen Thieu
Invariant manifolds of admissible classes for semi-linear evolution equations. (English)
[J] J. Differ. Equations 246, No. 5, 1820-1844 (2009). ISSN 0022-0396

This paper is a nice contribution to the study of asymptotic behavior of solutions of semilinear evolution equations. Using the characterization of the exponential dichotomy of evolution equations, the existence of invariant manifolds for the evolution equation is obtained under more general conditions on the nonlinear term $f$. And, the assumption of uniform Lipschitz continuity of the nonlinear term $f$ is actually replaced by its non-uniform Lipschitz continuity. Generally speaking, this is a good article being worth reading.
[Zhenbin Fan (Jiangsu)]

MSC 2000:: *34G20 Nonlinear ODE in abstract spaces
34C45 Method of integral manifolds

Keywords: evolution equations; integral equations; exponential dichotomy; admissibility of function spaces; local-stable manifolds; invariant manifolds of admissible classes

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Zentralblatt MATH Berlin [Germany]