Stepanov-like almost automorphic functions on time scales and the
application to cellular neural networks with time-varying delays
Abstract
In this work, we first propose the concept of stepanov-like almost
automorphic functions on time scales, and present some properties,
including the translation invariance and completeness. Moreover, we also
prove the connection between stepanov-like almost automorphic functions
on time scales and on $\mathbb{R}$. Then we establish
some existence and uniqueness result of almost automorphic solutions for
some linear dynamic equation on time scales. As an application of the
above results, we study the existence and global exponential stability
of almost automorphic solutions for a class of cellular neural networks
with time-varying delays on time scales.