一个n阶微分方程的两点边值问题

有一些n阶非线性微分方程的两点边值问题已被人们讨论过,大多是在微分方程的右端函数有界、满足李普希兹条件或在相应边值问题存在上下解的情况下讨论的。[3]、[4]在这篇文章里,讨论了一个n阶非线性微分方程的两点线性边值问题,是首先通过n-2次累次积分将原方程化成了一个二阶微积分方程边值问题,并用拓扑度理论讨论了解的存在性,同时给出了解的唯一性条件。推广了文献[1]的结果。     

n阶非线性常微分方程n点边值问题解的存在唯一性

n阶非线性常微分方程n点边值问题解的存在唯一性早在20世纪50年代就有人开始研究，所得结果都是在条件及其复杂，假设了一些边值问题解的存在性或唯一性(甚至包括其自身的)的基础上得到的，这给应用带来了困难。至今还没有人得到条件简单明了的便于应用的存在唯一性定理。这篇文章成功地将上述边值问题转化成了积分方程问题．并利用格林函数，不动点定理得到了较好的存在唯一性结果。为研究n阶非线性常微分方程非线性n点边值问题奠定了基础。     

两类n阶非线性方程的两点边值问题

已有人利用上下解方法讨论过非线性n阶常微分方程两点边值问题解的存在性，而边值问题是否存在上下解是很难判别的，在文中，用初等方法讨论了两类n阶非线性方程满足两点边界条件的边值问题解的存在性、唯一性，并对解的存在性唯一性区间进行了估计。     

非线性四阶微分方程两点边值问题解的存在唯一性

讨论了非线性四阶微分方程y(4)=f(x,y,y',y',y')的两点边值问题解的存在唯一性。其中,函数f在[a,b]×R4上连续,且满足Lipschitz条件。     

Banach空间中的常微分方程边值问题的拟上下解方法

利用拟上下解方法,研究了一阶非线性微分方程边值问题u′(t)=f(t,u(t)),u(0)-u(T)=x1,x1≥0拟解的存在性,并通过线性微分方程的解来构造算子,从而得到单调迭代序列,进而得到该边值问题的最大最小拟解对。     

四阶常微分方程两点边值问题解的存在性

利用上下解的方法,讨论了非线性四阶常微分方程y(4)=f(t,y,y',y″,y)满足条件g0(y(a),y'(a))=0,g1(y'(a),y″(a))=0,g2(y″(a),y(a))=0h(y(c),y'(c),y″(c),y(c))=0的非线性两点边值问题解的存在性,其中函数f,gi和h是具有一定单调性质的连续函数。     

一类非线性边值问题正解的存在性研究

为讨论一类非线性二阶两点边值问题正解的存在性,利用上下解方法,构造相应锥映射,给出非线性变号的二阶两点边值问题正解存在性的判定方法;对已发表文献中相应的结果进行推广,从而获得该类边值问题存在正解的重要结论。     

含双孔各向异性板的热应力集中

利用各向异性体平面热传导、热弹性理论中的复势方法,以保角映射和Faber级数为工具,导出了含双椭圆孔各向异性板热传导、热弹性的第一、二类边值问题的级数解,详细探讨了物理参数、几何参数对热应力集中的影响规律。     

一类二阶三点边值问题解的存在性

运用上下解方法,研究了一类二阶混合非线性边值条件的三点边值问题,通过构造了适当的非线性辅助函数工得到了解存在的充分条件,推广和改进了某些已知的结果。     

一类非线性三点边值问题正解的存在性

文章研究了一类非线性三点边值问题正解的存在性。运用一种新的方法得到格林函数的一些性质,然后运用Guo—Krasnoselskii不动点定理建立了边值问题在满足很弱的条件下解存在的条件,推广和改善了相关文献的结果。     

带电导体静电场等值面边值问题的边界积分方程

利用强极值原理将带电导静电场内，外等值面边值问题化为几个常规的椭圆型Dirichlet边值问题，并建立它们相应的第一类Fredholm边界积分方程，由这些方程的解的线性组合可构成原问题的解。     

2n阶边值问题的正解

通过运用锥不动点定理来讨论2n阶边值问题[multiply fro i=1 to n(-(d~2/dt~2) λ_i)]u=f(t,u),0-π2,i=1,2,…,n。f是非负连续函数。     

非线性热传导方程混合问题插值逼近

以Legendre-Gauss-type积分节点为插值节点,构造插值基函数展开数值解,逼近有界杆上的非线性热传导方程Dirichlet边界条件的正确解。给出算法格式和相应的数值算例,表明所提算法格式的有效性和高精度。所给算法适合于非线性问题求解。     

Fuel-optimal trajectories of aeroassisted orbital transfer withplane change

The fuel-optimal control problem arising in noncoplanar orbital transfer employing aeroassist technology is addressed. The mission involves the transfer from high Earth orbit to low Earth orbit with plane change. The complete maneuver consists of a deorbit impulse to inject a vehicle from a circular orbit to an elliptic orbit for atmospheric entry, a boost impulse at the exit from the atmosphere for the vehicle to attain a desired orbital altitude, and a reorbit impulse to circularize the path of the vehicle. In order to minimize the total fuel consumption, a performance index is chosen as the sum of the deorbit, boost, and reorbit impulses. The application of optimization principles leads to a nonlinear, two-point, boundary value problem, which is solved by a multiple shooting method     

Marangoni boundary layers

This paper deals with the theory of Marangoni boundary layers developing near the free surface of a nonuniformly heated liquid.

In the Introduction the notion of a thermocapillary effect is considered, and the conditions, under which thermocapillary flow is dominant, are elucidated. The similarity criteria of the problems are revealed, and the effects resulting from melt convection are considered.

In the second section the mathematical aspects of the theory of Marangoni boundary layers are considered. The boundary layer effect on the form of a free surface is investigated, and some examples are presented.

In Section 3 a qualitative flow pattern in a Marangoni boundary layer is analyzed, similarities and differences in the problems of Prandtl and Marangoni boundary layer theory are discussed. The possibility of Marangoni boundary layer degeneration at the outer boundary, as well as the initiation of flow containing a counter-stream zone are emphasized.

The fourth section outlines the calculation scheme on the basis of boundary-layer theory for convective flows with directed crystallization and in the absence of mass forces. Some examples are presented.

In the fifth section some problems of the theory of Marangoni boundary layers that need further investigation are discussed.     

Analysis of nonlinear deformation and stability of reinforced elliptic cylindrical shells under bending with internal pressure

A finite element statement of solving problems on stability of reinforced elliptic cylindrical shells taking into account momentness and nonlinearity of their subcritical stress strain state is presented. The explicit expressions for displacements of noncircular cylindrical shell elements as rigid bodies are determined by integrating the equations obtained by equating the components of linear strains to zero. These expressions were used to construct the form functions for an efficient quadrilateral finite element of natural curvature. An efficient numerical algorithm of nonlinear deformation and stability of shells was developed. The stability of reinforced elliptic cylindrical shells under combined loading by bending moment, transverse boundary force and internal pressure is analyzed. We also examine how the critical loads are affected by the strain nonlinearity and ellipticity of shell deformation at the subcritical stage.