Existence and Stability of Almost Periodic Solutions of Differential Equations with Generalized Piecewise Constant Argument

Abstract: This work deals with the existence of an almost periodic solution for certain kind of differential equations with generalized piecewise constant argument, almost periodic coefficients which are seen as a perturbation of a linear equation of that kind satisfying an exponential dichotomy on a difference equation. The stability of that solution in a semi-axis studied.