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A Case of One-to-One Correspondence between Almost Automorphic and Asymptotically Almost Automorphic Solutions

Gaston M. N’Guerekata
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Gaston M. N’Guerekata: Morgan State University

Chapter Chapter 6 in Almost Automorphic and Almost Periodic Functions in Abstract Spaces, 2001, pp 93-97 from Springer

Abstract: Abstract Consider in a Banach space X the differential equation 6.1 $$x'(t) = Ax(t) + f(t)$$ and the nonlinear differential equation 6.2 $$x'(t) = Ax(t) + f(t) + g(t,x(t))$$ where A is the infinitesimal generator of a C 0-group T = (T(t)) t∈ℝ of bounded linear operators X → X,with sup t∈ℝ ||T(t)|| = M

Date: 2001
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DOI: 10.1007/978-1-4757-4482-8_6

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