Measure pseudo almost periodic solutions for differential equations with reflection

ABSTRACT

In this research paper, we give some new results for the existence and uniqueness of doubly measure pseudo almost periodic (Or $(\mu ,\nu )$-pap) solutions for some differential equations with reflection. We will use the Banach fixed-point theorem and some properties of pseudo almost periodic functions with measurements and we will discuss both linear and nonlinear cases. Finally, we finish with some applications to illustrate our results.

Keywords:

• Pseudo almost periodic
• ergodic
• differential equations with reflection
• positive measure

AMS Subject Classifications:

• 34K30
• 35B15

Disclosure statement

No potential conflict of interest was reported by the author(s).