A Study on PC Pseudo almost Automorphic Solution of Impulsive Differential Equation

Soumya George, Kavitha Velusamy and Grayna Jeyakumar

This manuscript extends the idea of Pseudo almost Automorphic(𝒫𝒫𝒫𝒫𝒫𝒫) functions to Piecewise Continuous (PC)-𝒫𝒫𝒫𝒫𝒫𝒫 functions in the framework of impulsive systems. Some important properties of PC- 𝒫𝒫𝒫𝒫𝒫𝒫 functions are established. Utilizing these properties and Sadovskii fixed point theorem, we prove existence and uniqueness theorem for PC-𝒫𝒫𝒫𝒫𝒫𝒫 mild solutions to impulsive differential equations in a Banach space. Suitable examples are given to exhibit our analytic findings.

Volume 11 | 11-Special Issue

Pages: 788-799

DOI: 10.5373/JARDCS/V11SP11/20193097