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Invariant manifolds of admissible classes for semi-linear evolution equations. (English) Zbl 1178.34070
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.

34G20Nonlinear ODE in abstract spaces
34C45Invariant manifolds (ODE)
Full Text: DOI
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