Existence and Uniqueness of Almost Automorphic Mild Solutions to Some Semilinear Abstract Differential Equations
Existence and Uniqueness of Almost Automorphic Mild Solutions to Some Semilinear Abstract Differential Equations
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DOI：
10.1007/s00233-003-0021-0
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发表时间：
2004-03
期刊：
影响因子：
0.7
通讯作者：
G. N’Guérékata
中科院分区：
文献类型：
--
作者：
G. N’Guérékata
考虑Banach空间X中的半线性微分方程x‘(T)=Ax(T)+f(t，x(T))，t∈ℝ，其中A是指数稳定的C0半群的非负生成元.在f上适当的条件下，证明了该方程存在唯一的几乎自同构的温和解。
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.