Almost automorphic solutions to nonautonomous semilinear evolution equations in Banach spaces

作者：Ding, Hui-Sheng; Liang, Jin; Xiao, Ti-Jun^*

来源：Nonlinear Analysis-Theory Methods & Applications, 2010, 73(5): 1426-1438.

DOI：10.1016/j.na.2010.05.006

• Almost automorphic
• Pseudo-almost automorphic
• Stepanov-like almost automorphic
• Semilinear evolution equation
• Evolution family

This paper is concerned with almost automorphy of the solutions to a nonautonomous semilinear evolution equation u'(t) = A(t)u(t) +f(t, u(t)) in a Banach space with a Stepanov-like almost automorphic nonlinear term. We establish a composition theorem for Stepanov-like almost automorphic functions. Furthermore, we obtain some existence and uniqueness theorems for almost automorphic solutions to the nonautonomous evolution equation, by means of the evolution family and the exponential dichotomy. Some results in this paper are new even if A(t) is time independent.

• 出版日期2010-9-1
• 单位江西师范大学; 复旦大学; 上海交通大学