Dichotomy and μ‐pseudo almost automorphic solutions for delayed partial functional differential equations in admissible spaces

Chiraz Jendoubi

Mathematische Nachrichten, 2021, vol. 294, issue 2, 338-353

Abstract: We prove the existence and uniqueness of μ‐pseudo almost automorphic 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. We further prove the existence of an invariant stable manifold around the μ‐pseudo almost automorphic solution in that case. An application is given to illustrate our theory.

Date: 2021
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