Weakly decaying energy separation and uniqueness of motions of an elastic-plastic oscillator with work-hardening (Q1820618)

The motion of elastic-plastic oscillator with work-hardening is studied. The forced motions of a mass supported by an element of this type are described by a system of three ordinary differential equations along with an inequality constraint. According to the author the problem of uniqueness requires a new strategy. This strategy requires that the energy separation of solutions decays weakly in time in the sense that the initial energy separation never is exceeded by its subsequent values. Thus, the energy separation can decay weakly and still increase on certain intervals, as long as each increase is compensated by a priori decrease of the same or greater magnitude.