Banach空间中半线性非自治微分方程的概自守解

Almost Automorphic Solution for Semilinear Non-autonomous Differential Equations in Banach Spaces

摘要

摘要:讨论 Banach空间中半线性非自治微分方程的概自守解.首先,利用发展系统理论证明半线性非自治微分方程的概自守解的存在性和唯一性.其次,利用 Banach不动点定理,证明非自治微分方程的概自守解的存在性和唯一性.

Abstract:An investigation was made into the almost automorphic solution for the semi-linear non-autonomous differential equations in Banach spaces. By theory of evolution family, the existence and uniqueness of the almost automorphic solution for the semi-linear non-autonomous differential equation ddtu(t) = A(t)u(t)+h(t) is proved. Then by Banach fixed point theo- rem, the existence and uniqueness of the almost automorphic solution for the semi-linear non-autonomous differential equation dtu(t) = A(t)u(t) +f(t,u(t)) is also proved.