非自治中立型无穷时滞泛函微分方程的加权伪概自守解

首先引入h型Stepanov 加权伪概自守函数和∞型Stepanov加权伪概自守函数的概念, 接着建立了其函数空间的完备性以及相应组合定理, 最后证明了一类非自治无穷时滞偏中立型泛函微分方程在S^p-加权伪概自守系数下加权伪概自守解的存在唯一性.

Weighted pseudo almost automorphic solutions for non-autonomous neutral functional differential equations with infinite delay

We first introduce the notion of Stepanov-like weighted pseudo almost automorphic functions of class h and the notion of Stepanov-like weighted pseudo almost automorphic functions of class ∞, and then establish some basic results not only on the completeness of the space that consists of the S^p-weighted pseudo almost automorphic functions of class h and class ∞ but also on the compositions of such functions. Finally, we apply the abstract results to prove the existence and uniqueness of weighted pseudo almost automorphic solutions with S^p-weighted pseudo almost automorphic coefficients to a non-autonomous first-order abstract partial neutral functional differential equation with infinite delay.