This work reports new approaches for order reduction of nonlinear systems with time periodic coefficients. First, the equations of motion are transformed using the Lyapunov-Floquet (LF) transformation, which makes the linear part of new set of equations time invariant. At this point, either linear or nonlinear order reduction methodologies can be applied. The linear order reduction technique is...

in this paper, sufficient conditions are investigated for the existence of periodic (not necessarily positive) solutions for nonlinear several time delay population system with feedback control. nonlinear system affected by an periodic external source is studied. existence of a control variable provides  the extension of  some previous results obtained in other studies. we give a illustrative e...

We consider the operator H = d 4 dt4 + d dtp d dt + q with 1-periodic coefficients on the real line. The spectrum of H is absolutely continuous and consists of intervals separated by gaps. We describe the spectrum of this operator in terms of the Lyapunov function, which is analytic on a two-sheeted Riemann surface. On each sheet the Lyapunov function has the standard properties of the Lyapunov...

Most research on order splitting have focused on the reduction of safety stock in the multiple sourcing setting. Moreover, all works study the use of order splitting for the continuous review inventory systems. In this paper, we investigate the possibility of the multiple-delivery arrangement in the sole sourcing environment. In addition, we concentrate on the reduction of cycle stock for perio...

We provide sufficient conditions for the existence of periodic solutions of the second order Hamiltonian system −x′′ − λx = εV ′ x (t, x) , where ε is a small parameter, x ∈ R and V (t, x) is 2π-periodic in t. Moreover we provide two applications.

Existence of periodic solutions for non-linear third order autonomous differential equation (O.D.E.) has not been investigated to as large an extent as non-linear second order. The popular Poincare-Bendixon theorem applicable to second order equation is not valid for third order equation (see [3]). This conclusion opens a way for further investigation.