Pseudo almost automorphic solutions for some partial functional differential equations with infinite delay

Abstract

In this work, we study the existence of pseudo almost automorphic solution for some partial functional differential equations with infinite delay. We assume that the undelayed part is not necessarily densely defined and satisfies the Hille–Yosida condition. We use the variation of constant formula developed recently in 1 to get the existence and uniqueness of pseudo almost automorphic solution when the linear equation has an exponential dichotomy. We also give an application of the abstract results to a Lotka–Volterra model with diffusion.

Keywords:

• Hille–Yosida condition
• infinite delay
• c₀-semigroup
• integral solution
• fading memory space
• pseudo almost automorphic solution
• exponential dichotomy

AMS Subject Classifications:

• 34C27
• 34K14
• 35R10