Existence and stability of almost periodic solutions of nonlinear damped equations of a suspended string (Q447803)

In this paper, instead of the Fourier expansion method in both \(x\), \(t\), the authors combine the Fourier expansion method with respect to \(x\) with the representation formula of the almost periodic solutions of the second-order scalar ODE with almost periodic forcing term. Using this method in some well-defined function space, they obtain the existence and uniqueness of an almost periodic solution of a linear BVP with \(\epsilon=0\) and the basic energy estimates of the solution in suitable function space of almost periodic functions.