Pseudo almost periodic solutions for a class of nonlinear Duffing equations on time scales.

In this paper, we study the pseudo almost periodic solutions for a class of nonlinear Duffing equations with S p -pseudo almost periodic coefficients and delays on time scales. For this purpose, we establish a result of the existence and uniqueness of pseudo almost periodic solution for an abstract linear equation with S p -almost periodic coefficients and S p -pseudo almost periodic forcing term. Meanwhile, to deal with the delay, we extend some concepts of functions from T → R to T → Π , where T is a time scale with translation set Π , and give some basic properties for these concepts. Then, applying these results, we obtain some results on the existence and uniqueness of pseudo almost periodic solutions for the Duffing equation. Moreover, some examples are given to illustrate our main results. [ABSTRACT FROM AUTHOR]