Pseudo almost automorphic solutions of class \(r\) in \(\alpha\)-norm under the light of measure theory (Q2023276)

The authors study the existence of pseudo almost automorphic solutions using the alpha-norm for some partial functional differential equations. The linear part is assumed to generate a compact analytic semigroup, the input function is almost automorphic. The authors assumed that the linear partial functional differential equation is hyperbolic. This assumption allows them to use a formula for bounded solutions and to prove the existence of pseudo almost automorphic solutions for the whole system. Some result are also given for nonlinear systems using the Banach fixed point theorem.