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Periodic systems dependent on parameters. (English) Zbl 1198.35135

Summary: This paper is concerned with a periodic system dependent on parameters. We study the differentiability with respect to parameters of the periodic solution of the system. Applying a fixed point theorem and the results regarding parameters for \(C_0\)-semigroups, we obtain some convenient conditions for determining differentiability with parameters of the periodic solution. The paper is concluded with an application of the obtained results to a periodic boundary value problem.

MSC:

35K90 Abstract parabolic equations
47D06 One-parameter semigroups and linear evolution equations
35K20 Initial-boundary value problems for second-order parabolic equations
35B10 Periodic solutions to PDEs
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References:

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