𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Almost automorphic solutions to nonautonomous semilinear evolution equations in Banach spaces

✍ Scribed by Hui-Sheng Ding; Jin Liang; Ti-Jun Xiao

Publisher
Elsevier Science
Year
2010
Tongue
English
Weight
370 KB
Volume
73
Category
Article
ISSN
0362-546X

No coin nor oath required. For personal study only.

✦ Synopsis

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.

πŸ“œ SIMILAR VOLUMES

Almost automorphic and pseudo-almost aut
Almost automorphic and pseudo-almost automorphic mild solutions to an abstract differential equation in Banach spaces
✍ Zhi-Han Zhao; Yong-Kui Chang; Juan J. Nieto πŸ“‚ Article πŸ“… 2010 πŸ› Elsevier Science 🌐 English βš– 515 KB

In this paper we prove some existence results for almost automorphic and pseudo-almost automorphic mild solutions to a class of abstract differential equations in Banach spaces. The main technique is based on some composition theorems combined with the contraction mapping theorem. Finally, we presen