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Existence and Uniqueness of Almost Automorphic Mild Solutions to Some Semilinear Abstract Differential Equations

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Abstract

We consider the semilinear differential equation x’(t) = Ax(t) + f(t, x(t)), t ∈ ℝ in a Banach space X, where A is the in.nitesimal generator of an exponentially stable C0-semigroup. Under suitable conditions on f, we prove the existence and uniqueness of an almost automorphic mild solution to the equation.

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  1. Department of Mathematics, Morgan State University, 1700 E. Cold Spring Lane, Baltimore, MD 21251, USA

    Gaston M. N’Guérékata

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  1. Gaston M. N’Guérékata
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Correspondence to Gaston M. N’Guérékata.

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Edited by M. Putcha

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N’Guérékata, G. Existence and Uniqueness of Almost Automorphic Mild Solutions to Some Semilinear Abstract Differential Equations. Semigroup Forum 69, 80–86 (2004). https://doi.org/10.1007/s00233-003-0021-0

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  • DOI: https://doi.org/10.1007/s00233-003-0021-0

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