一类二阶微分方程无穷边值问题的可解性

研究了一类无穷区间上非线性二阶微分方程两点边值问题解的存在性.首先在连续函数空间中引入算子T,并证明了T是全连续算子,然后利用Banach空间上全连续算子的不动点定理等方法,得到了这类边值问题存在有界解的一个充分条件,从而证明了一类无穷区间上非线性二阶微分方程两点边值问题的可解性,文末举例说明了定理的可行性.     

带有p-Laplace算子的分数阶边值问题的特征区间（英文）

本文研究了一类带有p-Laplace算子的分数阶微分方程两点边值问题.利用锥上的不动点定理,得到了这类边值问题的特征区间,推广了整数阶边值问题情形的结论.     

带有p-Laplace算子的分数阶边值问题的特征区间

本文研究了一类带有p-Laplace算子的分数阶微分方程两点边值问题.利用锥上的不动点定理,得到了这类边值问题的特征区间,推广了整数阶边值问题情形的结论.     

半正的分数阶微分方程(n-1,1)-型积分边值问题的多个正解

采用Riemann-Liouville分数阶导数,研究了半正的分数阶微分方程(n-1,1)-型积分边值问题,获得了参数λ的一个区间,使得λ落在这个区间的时候,该半正的分数阶微分方程边值问题有多个正解.     

变时滞二阶奇异边值问题的正解和特征区间

基于锥上不动点定理,研究了变时滞二阶奇异边值问题,用算子逼近的方法处理奇异性,在较弱的条件下,得到了正解的存在性和特征区间.     

无穷区间上具有p-Laplacian算子边值问题的正解

研究了一类在无穷区间上具有p-Laplacian算子的边值问题的迭代正解.利用单调迭代方法得到问题的迭代正解存在性的充分条件,同时得到了解的相应迭代序列,最后给出例子证明所得结论.     

具非自治微小扰动的脉冲方程三个古典解的存在性

在半直线无穷区间上,我们研究具有微小非自治扰动项的脉冲方程边值问题的古典解,应用变分方法和相应的临界点理论得到了三个古典解的存在性.     

半无穷区间上具有共振的序列分数阶微分方程积分边值问题的可解性

本文研究半无穷区间上具有共振的分数阶微分方程积分边值问题.通过构造适当的Banach空间及算子,利用迭合度理论和Mawhin连续性定理获得上述边值问题解的存在性结论,推广了前人的结果.     

一类无穷区间上具有积分边界条件的分数阶微分方程的正解存在性

研究一类无穷区间上具有积分边界条件的分数阶微分方程边值问题.先构造Green函数,并讨论相关性质,再利用压缩映象原理及单调迭代法,讨论此类边值问题的正解存在性,建立了若干正解存在定理.     

一类奇异无穷边值问题正解的存在性

通过构造一个特殊的锥,利用不动点指数定理,研究了无穷区间上一类二阶奇异Stuem-Liouville边值问题,得到了其$C^1_p[0,\infty)$正解存在的一个判定方法.     

Discrete invariant imbedding for the numerical solution of boundary-value problems over infinite intervals

A numerical method to solve boundary-value problems posed on infinite intervals is given by reducing the infinite interval to a finite interval which is large, and impossing appropriate asymptotic boundary conditions at the far end. Then the two-point boundary-value problem is solved by using discrete invariant-imbedding method, which is also analyzed for its stability. The theory is illustrated by solving a test example.     

A nonlocal problem for singular linear systems of ordinary differential equations

A system of linear ordinary differential equations is examined on an infinite half-interval. This system is supplemented by the boundedness condition for solutions and a nonlocal linear condition specified by the Stieltjes integral. A method for approximating the resulting problem by a problem posed on a finite interval is proposed, and the properties of the latter are investigated. A numerically stable method for solving this problem is examined. This method uses an auxiliary boundary value problem with separated boundary conditions.     

The Airy equation with nonlocal conditions

We study a third-order dispersive linear evolution equation on the finite interval subject to an initial condition and inhomogeneous boundary conditions but, in place of one of the three boundary conditions that would typically be imposed, we use a nonlocal condition, which specifies a weighted integral of the solution over the spatial interval. Via adaptations of the Fokas transform method (or unified transform method), we obtain a solution representation for this problem. We also study the time periodic analog of this problem, and thereby obtain long time asymptotics for the original problem with time periodic boundary and nonlocal data.     

Banach空间中含有无穷多个跳跃点的一阶脉冲积分-微分方程的无穷边值问题

通过建立一个新的比较引理,应用上下解方法和单调迭代技术,研究了Banach空间中含有无穷多个跳跃点的一阶脉冲积分-微分方程无穷边值问题在任意闭区间上最小解和最大解的存在性.     

A numerical method for a system of equations with a small parameter and a point source on an infinite interval

A method for solving a boundary-value problem on an infinite interval is considered for a linear system of second-order ordinary differential equations with a small parameter at the highest derivatives and a point source. The question is addressed of reduction of this problem to a finite interval. A mesh, condensing in the boundary layer, is used for numerical solution of a system of singularly perturbed equations on a finite interval.     

Decay mode solution of nonlinear boundary–initial value problems for the cylindrical (spherical) Boussinesq–Burgers equations

The major target of this paper is to construct new nonlinear boundary–initial value problems for Boussinesq–Burgers Equations, and derive the solutions of these nonlinear boundary–initial value problems by the simplified homogeneous balance method. The nonlinear transformation and its inversion between the Boussinesq–Burgers Equations and the linear heat conduction equation are firstly derived; then a new nonlinear boundary–initial value problem for the Boussinesq–Burgers equations with variable damping on the half infinite straight line is put forward for the first time, and the solution of this nonlinear boundary–initial value problem is obtained, especially, the decay mode solution of nonlinear boundary–initial value problem for the cylindrical (spherical) Boussinesq–Burgers equations is obtained.     

Stokes' first problem for a Newtonian fluid in a non‐Darcian porous half‐space using a Laguerre–Galerkin method

A Laguerre–Galerkin method is proposed and analysed for the Stokes' first problem of a Newtonian fluid in a non‐Darcian porous half‐space on a semi‐infinite interval. It is well known that Stokes' first problem has a jump discontinuity on boundary which is the main obstacle in numerical methods. By reformulating this equation with suitable functional transforms, it is shown that the Laguerre–Galerkin approximations are convergent on a semi‐infinite interval with spectral accuracy. An efficient and accurate algorithm based on the Laguerre–Galerkin approximations of the transformed equations is developed and implemented. Numerical results indicating the high accuracy and effectiveness of this algorithm are presented. Copyright © 2007 John Wiley & Sons, Ltd.     

On the moving boundary formulation for parabolic problems on unbounded domains

A parabolic problem defined on unbounded domains and admitting invariance property to Lie group of scalings can be transformed into an equivalent boundary value problem governed by an ODE defined on an infinite interval. A free boundary formulation and a convergence theorem for this kind of transformed problems are available in [Fazio, SIAM J. Numer. Anal., 33 (1996), pp. 1473-1484]. Depending on its scaling invariance properties, the free boundary problem is then solved numerically using either an iterative or a non-iterative method. Finally, the solution of the parabolic problem is retrieved applying the inverse map of similarity. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Singular perturbation of an infinite interval linear state regulator problem in optimal control

The corresponding problem on a finite interval has been studied by O'Malley and Kung using two different methods, namely: (1) the two-point boundary value method (O'Malley and Kung, SIAM J. Control13 (1975), 327–337) and (2) The Riccati gain method (O'Malley and Kung, J. Differential Eqs.16 (1974), 413–427). For the infinite interval, the two-point boundary value method is no longer relevant. However, the Riccati gain method can be applied. The conditions are changed slightly from those for the finite interval case. Some conditions are eliminated and some new conditions are added.     

A CLASS OF SINGULAR PERTURBATIONS FOR SECOND ORDER QUASI－LINEAR BOUNDARY VALUE PROBLEMS ON INFINITE INTERVAL

ＡＣＬＡＳＳＯＦＳＩＮＧＵＬＡＲＰＥＲＴＵＲＢＡＴＩＯＮＳＦＯＲＳＥＣＯＮＤＯＲＤＥＲＱＵＡＳＩ－ＬＩＮＥＡＲＢＯＵＮＤＡＲＹＶＡＬＵＥＰＲＯＢＬＥＭＳＯＮＩＮＦＩＮＩＴＥＩＮＴＥＲＶＡＬＺＨＡＯＷＥＩＬＩ（赵为礼）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈ...