Existence and control of weighted pseudo almost periodic solutions for abstract nonlinear vibration systems

In many vibration problems, it is very important to know precisely the bounds of the stability/instability frequencies and the associated amplitude ranges. This paper investigates the solvability and control of some weighted pseudo almost periodic solutions of abstract nonlinear vibration differential systems. Some sufficient conditions for the solvability and exponential stability of these systems are obtained. Moreover, the precise bound of Lyapunov exponents is estimated