Periodic traveling waves of a mean curvature equation in high dimensional cylinders

Let Ω be the unit ball in R^N. Consider the mean curvature equation

(E0)     

A continuation theorem on periodic solutions of regular nonlinear systems and its application to the exact tracking problem for the inverted spherical pendulum

We present a continuation method to obtain a family of T-periodic solutions for a family of T-periodic systems.In particular, we present some sufficient analytical conditions, which have the advantage of being an easy application to some systems of interest in physics or engineering. We apply these conditions to the exact tracking problem for the inverted spherical pendulum.     

Fourier expansion based recursive algorithms for periodic Riccati and Lyapunov matrix differential equations

Combining Fourier series expansion with recursive matrix formulas, new reliable algorithms to compute the periodic, non-negative, definite stabilizing solutions of the periodic Riccati and Lyapunov matrix differential equations are proposed in this paper. First, periodic coefficients are expanded in terms of Fourier series to solve the time-varying periodic Riccati differential equation, and the state transition matrix of the associated Hamiltonian system is evaluated precisely with sine and cosine series. By introducing the Riccati transformation method, recursive matrix formulas are derived to solve the periodic Riccati differential equation, which is composed of four blocks of the state transition matrix. Second, two numerical sub-methods for solving Lyapunov differential equations with time-varying periodic coefficients are proposed, both based on Fourier series expansion and the recursive matrix formulas. The former algorithm is a dimension expanding method, and the latter one uses the solutions of the homogeneous periodic Riccati differential equations. Finally, the efficiency and reliability of the proposed algorithms are demonstrated by four numerical examples.     

Existence of periodic solutions for a class of first order delay differential equations dealing with vectors

By the weak linking theorem and the local linking theorem, we study the existence of periodic solutions for the following delay non-autonomous systems

(1)     

On the empirical performance of (T, s, S) heuristics

The periodic (T,s,S)$(T\text{,}s\text{,}S)$ policies have received considerable attention from the academic literature. Determination of the optimal parameters is computationally prohibitive, and a number of heuristic procedures have been put forward. However, these heuristics have never been compared in an extensive empirical study. Such an investigation on 3055 SKUs is carried out in this paper. Our study provides insights into the performance of (T,s,S)$(T\text{,}s\text{,}S)$ heuristics, also in relation to demand forecasting. The results show that Naddor’s heuristic is best able to minimize the total cost. However, the normal and power approximations achieve more efficient solutions in that backorder volumes are smaller at the same inventory levels, indicating the potentially superior performance of these methods if the balancing of holding and backorder costs can be improved. The results also show that, for all heuristics, the SBA variant of the Croston forecasting method significantly outperforms Croston as well as Single Exponential Smoothing (SES).     

THE STABILITY OF THE PERIODIC SOLUTIONS OF SECOND ORDER HAMILTONIAN SYSTEMS

51.IntroductionandMainResultsInthispaper,weconsiderthestabilityoftheperiodicsolutionsofthefollowingsecondorderHamiltoniansystemswherenisapositiveillteger.V:Rxac-RisafUnctionandforT>0itisT-periodicforthevariablet.VJdenotesitsgradientwithrespecttox.Wenowstatethemainresultsofthispaper.Forthesuperquadraticcase)wehavethefollowingtwotheoremsTheorem1.1.SmposeVsatiSfiesthefollowingconditions:(VI)VEC'(RxR",R)andV(t T,x)=V(t,x),V(t,x)ERxR".(V2)ThereexistconstantSp>2andco>0suchthat0相似文献   

MULTIPLICITY OF PERIODIC SOLUTIONS OF DUFFING''''S EQUATIONS WITH LIPSCHITZIAN CONDITION MULTIPLICITY OF PERIODIC SOLUTIONS OF DUFFING''''S EQUATIONS WITH LIPSCHITZIAN CONDITION

1. IntroductionWe deal with the Duffing equationi g(x) ~ p(t), (1.1)where g(x), p(t) E C(R, R) and p(t) is periodic, whose least period is 27. The multiplicityof periodic solutions of Equation (l.1) has been widely studied since the 50s. In [1], T.Ding studied the multiplicity of periodic solutions of Equation (1.1) under the followingconditions.(gi) Let g(x) E C'(R, R), and let K be a positive constant, such that(gi) There exist two constallts Ac > 0 and MO > 0 such thatg(x) w~ > AO…     

高维非自治系统的周期解

本文利用指数型二分性理论和不动点方法考虑系统Ｘ＝ｆ（ｔ,ｘ）,Ｘ＝Ａ（ｔ,ｘ）ｘ＋ｂ（ｔ,ｘ）的周期解的存在性问题,其中Ａ（ｔ,ｘ）是ｎ×ｎ连续矩阵函数,ｆ（ｔ,ｘ）,ｂ（ｔ,ｘ）是ｎ维连续向量函数,且关于ｔ以ｗ＞０为周期,所得结果推广了王联和曾唯尧的结果．     

高阶非线性常微分方程组周期解的存在性

本文考虑非线性常微分方程组周期解的存在性,得到了周期解的Ｎａｇｕｍｏ型先验估计,由此在一般性条件下证明了方程组至少有一个Ｔ－周期解,