<b><i>C</i></b>^{<b><i>n</i></b>}-almost automorphic solutions for partial neutral functional differential equations

Abstract

In this work, we study the existence of C n -almost periodic solutions and C n -almost automorphic solutions (n ≥ 1), for partial neutral functional differential equations. We prove that the existence of a bounded integral solution on ℝ+ implies the existence of C n -almost periodic and C n -almost automorphic strict solutions. When the exponential dichotomy holds for the homogeneous linear equation, we show the uniqueness of C n -almost periodic and C n -almost automorphic strict solutions.