Buse, ConstantinLupulescu, Vasile2021-01-292021-01-292003-12-16Buse, C., & Lupulescu, V. (2003). Exponential stability of linear and almost periodic systems on Banach spaces. Electronic Journal of Differential Equations, 2003(125), pp. 1-7.1072-6691https://hdl.handle.net/10877/13176Let vƒ(·, 0) the mild solution of the well-posed inhomogeneous Cauchy problem v̇(t) = A(t)v(t) + ƒ(t), v(0) = 0 t ≥ 0 on a complex Banach space X, where A(·) is an almost periodic (possible unbounded) operator-valued function. We prove that vƒ(·, 0) belongs to a suitable subspace of bounded and uniformly continuous functions if and only if for each x ∈ X the solution of the homogeneous Cauchy problem u̇(t) = A(t)u(t), u(0) = x t ≥ 0 is uniformly exponentially stable. Our approach is based on the spectral theory of evolution semigroups.Text7 pages1 file (.pdf)enAttribution 4.0 InternationalAlmost periodic functionsUniform exponential stabilityEvolution semigroupsArticle