Longtime behavior for oscillations of an extensible viscoelastic beam with elastic external supply

This work is focused on a nonlinear equation describing the oscillations of an extensible viscoelastic beam with fixed ends, subject to distributed elastic external force. For a general axial load $β$, the existence of a finite/infinite set of stationary solutions and buckling occurrence are scrutinized. The exponential stability of the straight position is discussed. Finally, the related dynamical system in the history space framework is shown to possess a regular global attractor.