Multiple doubly periodic solutions of semi-linear damped beam equations

The purpose of this work is to investigate the weakened Ambrosetti–Prodi type multiplicity results for weak doubly periodic solutions of damped beam equations. By using the topological degree theory, the author obtains a result which is similar to the result for damped wave equations in the literature.     

Estimates for Elements of Inverse Matrices for a Class of Operators with Matrices of Special Structure

In this paper, we consider questions related to the structure of inverse matrices of linear bounded operators acting in infinite-dimensional complex Banach spaces. We obtain specific estimates of elements of inverse matrices for bounded operators whose matrices have a special structure. Matrices are introduced as special operator-valued functions on an index set. The matrix structure is described by the behavior of the given function on elements of a special partition of the index set. The method used for deriving the estimates is based on an analysis of Fourier series of strongly continuous periodic functions.     

脉冲微分方程的上、下解及其在常微分方程上的应用

In this paper, we establish the existence of upper and lower solutions for a periodic boundary value problems (PBVP for short) of impulsive differential equations. which guarantees the existence of at least one solution for the problem. As an application, these results are applied to PBVP of ODE and some examples are given to illustrate our results.     

On the excitation of a closely spaced array by a line source

An infinite row of periodically spaced, identical rigid circularcylinders is excited by an acoustic line source which is parallelto the generators of the cylinders. A method for calculatingthe scattered field accurately and efficiently is presented.When the cylinders are sufficiently close together, Rayleigh–Blochsurface waves that propagate energy to infinity along the arrayare excited. An expression is derived which enables the amplitudesof these surface waves to be computed without requiring thesolution to the full scattering problem.     

New Jacobian Elliptic Function Solutions of Modified KdV Equation: Ⅱ

Recently, we obtained thirteen families of Jacobian elliptic function solutions of mKdV equation by usingour extended Jacobian elliptic function expansion method. In this note, the mKdV equation is investigated and anotherthree families of new doubly periodic solutions (Jacobian elliptic function solutions) are fbund again by using a newtransformation, which and our extended Jacobian elliptic function expansion method form a new method still called theextended Jacobian elliptic function expansion method. The new method can be more powertul to be applied to othernonlinear differential equations.     

EFFICIENT SIXTH ORDER P-STABLE METHODS WITH MINIMAL LOCAL TRUNCATION ERROR FOR y"=f(x,y)

1. IntroductionWe consider a class of direct hybrid methods proposed in [11 for solving the second orderinitial value problemy" = f(t,y), y(0),y'(0) given (1.1)The basic method has the formandHere t. = nh and we define t.l.. = t. I aih, i = 1, 2 and n=0,1…     

OPTIMAL HARVESTING POLICY FOR INSHORE-OFFSHORE FISHERY MODEL WITH IMPULSIVE DIFFUSION

This article studies the inshore-offshore fishery model with impulsive diffusion. The existence and global asymptotic stability of both the trivial periodic solution and the positive periodic solution are obtained. The complexity of this system is also analyzed. Moreover, the optimal harvesting policy are given for the inshore subpopulation, which includes the maximum sustainable yield and the corresponding harvesting effort.     

On existence and regularity of solutions for 2‐D micropolar fluid equations with periodic boundary conditions

In this paper, we prove the existence and uniqueness of a global solution for 2‐D micropolar fluid equation with periodic boundary conditions. Then we restrict ourselves to the autonomous case and show the existence of a global attractor. Copyright © 2006 John Wiley & Sons, Ltd.     

开关布局中本质不同的开关线路计算

通过对开关布局问题的研究，来解决一类象开关线路一样比较特殊，比较复杂的布局优化问题。从而寻找出这类问题的全局优化算法。本应用对称群对集合的作用，轨道，不动点等讨论了开关布局问题，给出了本质不同的开关线路个数的计算公式。     

Banach空间二阶周期边值问题解的存在性

利用一些比较结果，讨论了Banach空间中二阶周期边值问题解的存在性，获得了若干解的存在性与唯一性结果。