Exponential Dichotomy and Eberlein-Weak Almost Periodic Solutions

• 作者: Elhadi Ait Dads Lahcen Lhachimi Samir Fatajou
• 来源期刊: 应用数学(英文)
• 学科: 数学
• 关键词: Bounded Solutions ALMOST PERIODIC and Eberlein WEAK ALMOST PERIODIC Functions Exponential DICHOTOMY Linear Differential Equations
• 年，卷（期）: yysxyw_2012,（9）
• 页码范围: 969-975
• 页数: 7页
• 分类号: O1

摘要

We give sufficient conditions ensuring the existence and uniqueness of an Eberlein-weakly almost periodic solution to the following linear equation dx/dt(t) = A(t)x(t) + f(t) in a Banach space X, where (A(t)) t ∈□ is a family of infinitesimal generators such that for all t ∈□, A(t + T) = A(t) for some T > 0, for which the homogeneuous linear equation dx/dt(t) = A(t)x(t) is well posed, stable and has an exponential dichotomy, and f:□ →X is Eberlein-weakly amost periodic.