Cⁿ-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.

Keywords:

• Partial neutral functional differential equations
• Integral solution
• Strict solution
• Reduction principle
• C ⁿ -almost periodic solution
• C ⁿ -almost automorphic solution
• Exponential dichotomy

Keywords:

• Mathematics Subject Classifications: 34C27
• 34K14
• 34R10