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A class of singularly perturbed evolution systems. (English) Zbl 0805.34071

Summary: We study a class of evolution equations where the semigroup generators are singularly perturbed by a nonnegative real valued function of time. Sufficient conditions for existence of evolution operators and their compactness are given including continuous dependence on the perturbation. Further, for a coupled system of singular perturbed semilinear systems in two Banach spaces, existence of periodic solutions and their stability are studied.

MSC:

34K30 Functional-differential equations in abstract spaces
34C25 Periodic solutions to ordinary differential equations
34G20 Nonlinear differential equations in abstract spaces
34K20 Stability theory of functional-differential equations
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
34D15 Singular perturbations of ordinary differential equations
47D03 Groups and semigroups of linear operators
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