Almost automorphy of minimal sets for C1${C}∧{1}$-smooth strongly monotone skew-product semiflows on Banach spaces

We focus on the presence of almost automorphy in strongly monotone skew-product semiflows on Banach spaces. Under the C1$C<^>1$-smoothness assumption, it is shown that any linearly stable minimal set must be almost automorphic. This extends the celebrated result of Shen and Yi [Mem. Amer. Math. Soc. 136(1998), No. 647] for the classical C1,alpha$C<^>{1,\alpha }$-smooth systems. Based on this, one can reduce the regularity of the almost periodically forced differential equations and obtain the almost automorphic phenomena in a wider range.