Cn-Almost Periodic Functions and an Application to a Lasota-Wazewska Model on Time Scales

Abstract

We first give the definition and some properties of $C^n$-almost periodic functions on time scales. Then, as an application, we are concerned with a class of Lasota-Wazewska models on time scales. By means of the fixed point theory and differential inequality techniques on time scales, we obtain some sufficient conditions ensuring the existence and global exponential stability of $C^1$-almost periodic solutions for the considered model. Our results are essentially new when $\mathbb{T}=\mathbb{R}$ or $\mathbb{T}=\mathbb{Z}$. Finally, we present a numerical example to show the feasibility of obtained results.