Integral Inequalities and Pseudo Almost Automorphic Solutions to Semilinear Differential Equations in Banach Spaces

This work aims to investigate the existence and uniqueness of pseudo almost automorphic solutions to semilinear differential equations in Banach space. By generalizing the Bihari type inequality and using Krasnoselski–Schaefer fixed point theorem, the existence results are deduced. Moreover, a new estimate is also built to ensure the existence and uniqueness of solutions. An example is given to illustrate our conclusions.