Pseudo asymptotically Bloch periodic functions: applications for some models with piecewise constant argument (Q6539348)

The aim of this paper is to prove the existence and uniqueness of a pseudo asymptotically Bloch periodic solution for some evolution equation with piecewise constant argument. The system is governed by a linear part that generates an exponentially \(C_0\)-semigroup. The piecewise part is governed by a bounded linear operator. The input function is assumed to be pseudo asymptotically Bloch periodic. The authors use the fact that the \(C_0\)-semigroup is exponentially stable to prove the main results of this work. The same main theorem is obtained for nonautonomous evolution equations, governed by an evolution family that is exponentially stable.