On a viscoelastic plate equation with history setting and perturbation of p-Laplacian type

This paper is concerned with a class of plate equations with memory in a history space setting and perturbations of p-Laplacian type
$${u_{tt} + \alpha \Delta ^2u - \Delta _pu - \int_{-\infty }^{t} \mu(t -s) \Delta ^2u(s)ds - \Delta u_t + f(u) = h,}$$
defined in a bounded domain of
${\mathbb {R}^N }$
with simply supported boundary condition. Results on the well-posedness and asymptotic stability of the problem are proved.