Bohr-Neugebauer property for almost automorphic partial functional differential equations

ABSTRACT

We prove that a partial functional differential equation with infinite delay has the Bohr–Neugebauer property, when the semigroup generated by the differential operator is immediately compact and when the phase space has the uniform fading memory property. To illustrate our main result, we propose an application to a reaction–diffusion equation with continuous delay.

KEYWORDS:

• Infinite delay
• Bohr–Neugebauer type theorem
• almost automorphic solutions
• semigroup
• partial functional differential equations

AMS SUBJECT CLASSIFICATIONS:

• 34C27
• 35B15
• 35R10

Notes

No potential conflict of interest was reported by the authors.