This paper deals with the existence of solutions of the periodic boundary value problem of the impulsive Duffing equations: x′′ t αx′ t βx t f t, x t , x α1 t , . . . , x αn t , a.e. t ∈ 0, T , Δx tk Ik x tk , x′ tk , k 1, . . . , m, Δx′ tk Jk x tk , x′ tk , k 1, . . . , m, x i 0 x i T , i 0, 1. Sufficient conditions are established for the existence of at least one solution of above-mentioned ...

We seek the first indications that a nanoelectromechanical system (NEMS) is entering the quantum domain as its mass and temperature are decreased. We find them by studying the transition from classical to quantum behavior of a driven nonlinear Duffing resonator. Numerical solutions of the equations of motion, operating in the bistable regime of the resonator, demonstrate that the quantum Wigner...

Starting from an atomistic approach, we have derived a hierarchy of successively more simplified continuum elasticity descriptions for modeling the mechanical properties of suspended graphene sheets. We find that already for deflections of the order of 0.5 A a theory that correctly accounts for nonlinearities is necessary and that for many purposes a set of coupled Duffing-type equations may be...