μ-Pseudo almost periodic solutions for delayed partial functional differential equations in admissible spaces

Abstract

We present a theory of existence and uniqueness of μ-pseudo almost periodic solution for a delayed non-autonomous partial functional differential equation in the exponential dichotomic case, where the nonlinear operator F satisfies the ϕ-Lipschitz condition and ϕ belongs to some admissible spaces. Moreover, we prove the existence of an invariant stable manifold around the μ-pseudo almost periodic solution in that case. We give finally an application to illusrate our results.

Keywords:

• Partial functional differential equation
• admissibility of function spaces
• exponential dichotomy
• μ-pseudo almost periodic solution
• completeness
• composition theorem

AMS Subject Classifications:

• 34G20
• 34D09
• 47D06
• 34C27

Disclosure statement

No potential conflict of interest was reported by the authors.