TY - JOUR AU - Ji, Desheng AU - Lu, Yueming PY - 2015 DA - 2015/10/29 TI - Stepanov-like pseudo almost automorphic solution to a parabolic evolution equation JO - Advances in Difference Equations SP - 341 VL - 2015 IS - 1 AB - In this paper, the parabolic evolution equation $u'(t)+A(t)u(t)=f(t)$in a reflexive real Banach space is considered. Assuming strong monotonicity, pseudo almost automorphy and other appropriate conditions of the operators $A(t)$and Stepanov-like pseudo almost automorphy of the forced term $f(t)$, we obtain the Stepanov-like pseudo almost automorphy of the solution to the evolution equation by using the almost automorphic component equation method. This paper extends a known result in the case where $A(\cdot)$and f are almost automorphic in certain senses. Finally, a concrete example is given to illustrate our results. SN - 1687-1847 UR - https://doi.org/10.1186/s13662-015-0667-4 DO - 10.1186/s13662-015-0667-4 ID - Ji2015 ER -