椭圆型方程的内层和边界层渐近解

本文讨论了一类半线性椭圆型方程边值问题.利用微分不等式理论,研究了边值问题内层和边界层解的存在性和渐近性态.     

基于最高阶导数插值逼近的有理Sinc方法（英文）

为了求解不规则区域问题以及内部层的问题,讨论了一种基于最高阶导数插值逼近的Sinc有理插值方法.同时,给出了有理Sinc-barycentric插值公式,它可以有效地处理不规则区域上的混合边界条件.通过引入一个坐标变换,该方法被成功地应用于求解内层问题.数值实验证明该方法是有效的.     

拟线性方程Robin问题的内层和边界层解

本文讨论了一类拟线性方程Robin边值问题.利用微分不等式理论,研究了边值问题内层和边界层解的存在性和渐近性态.     

一类具有非整数幂的非线性奇异摄动内层问题

在适当的条件下,利用微分不等式以及内部层校正理论,研究了一类具有非整数幂的非线性奇异摄动内层问题．较简捷地证明了解的存在性,且对其解做出了估计,得出了其渐近解在[0,1]上的一致有效展开式．     

非线性方程激波位置的转移

本文是讨论一类非线性方程的激波位置.得出了在一定的情况下,当边界条件作微小的变化时,激波的位置将作较大的偏移,甚至由内层转到边界层.     

一类非线性方程激波位置的转移

讨论一类非线性方程的激波位置，得出了在一定的情况下，当边界条件作微小的变化时，激波的位置将作较大的偏移，甚至由内层转到边界层。     

奇摄动拟线性椭圆型方程边值问题的内层现象

本文研究一类奇摄动拟线性椭圆型方程Dirichlet问题的内层现象,利用偏微分不等式理论,通过构造具有内层校正的上、下解函数,给出了奇摄动问题内层现象的解的存在性及其余项估计。     

具有转向点的奇摄动非线性边值问题的非单调内部层性质

本文在ｆｙ（０，ｙ，ｙ＇）＝０（对所有ｙ，ｙ＇），即ｆ在ｔ＝０具有转向点的主要假设下研究非线性奇摄动问题εｙ＇＇＝ｆ（ｔ，ｙ，ｙ＇），ｙ（－１，ε）＝Ｂ，对充分小的ε＞０，建立了在转向点ｔ＝０呈两类非单调向部层（尖层或非单调过渡层）性态的解的存在性准则。     

一类有转向点的奇摄动非线性边值问题的内层性态

研究了一类具有转向点的非线性边界条件下的二阶非线性方程奇摄动问题.在退化方程的解是(Iq)(或(IIn)或(IIIn))稳定等条件下,利用微分不等式理论证明呈内层性态的解的存在性,并给出了解的渐近估计.     

数形结合解复合函数的零点个数的常见解法

本文通过利用函数图像的方法研究复合函数y=g（f（x））的零点问题,即复合函数方程g（f（x））=0的根,令u=f（x）（内层方程）,这样g（f（x））=0就转化成g（u）=0.当外层方程g（u）=0容易求解时,可以先解方程g（u）=0,再解内层方程u=f（x）,这样方程的总个数即为复合函数y=g（f（x））的零点个数.     

Nonmonotone Interior Layer Solutions for Singularly Perturbed Semilinear Boundary Value Problems with a Turning Point

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THE INTERIOR LAYER SOLUTION TO NONLOCAL REACTION DIFFUSION EQUATIONS

An initial boundary value problem of semilinear nonlocal reaction diffusion equations is considered.Under some suitable conditions,using the asymptotic theory,the existence and asymptotic behavior of the interior layer solution to the initial boundary value problem are studied.     

A CLASS OF STRONGLY NONLINEAR SINGULARLY PERTURBED INTERIOR LAYER PROBLEMS

In this paper, a class of strongly nonlinear singularly perturbed interior layer problems are considered by the theory of differential inequalities and the corrective theory of interior layer. The existence of solution is proved and the asymptotic behavior of solution for the boundary value problems are studied. And the satisfying result is obtained.     

Nonmonotone projected gradient methods based on barrier and Euclidean distances

We consider nonmonotone projected gradient methods based on non-Euclidean distances, which play the role of barrier for a given constraint set. Our basic scheme uses the resulting projection-like maps that produces interior trajectories, and combines it with the recent nonmonotone line search technique originally proposed for unconstrained problems by Zhang and Hager. The combination of these two ideas leads to produce a nonmonotone scheme for constrained nonconvex problems, which is proven to converge to a stationary point. Some variants of this algorithm that incorporate spectral steplength are also studied and compared with classical nonmonotone schemes based on the usual Euclidean projection. To validate our approach, we report on numerical results solving bound constrained problems from the CUTEr library collection.     

Affine scaling inexact generalized Newton algorithm with interior backtracking technique for solving bound-constrained semismooth equations

We develop and analyze an affine scaling inexact generalized Newton algorithm in association with nonmonotone interior backtracking line technique for solving systems of semismooth equations subject to bounds on variables. By combining inexact affine scaling generalized Newton with interior backtracking line search technique, each iterate switches to inexact generalized Newton backtracking step to strict interior point feasibility. The global convergence results are developed in a very general setting of computing trial steps by the affine scaling generalized Newton-like method that is augmented by an interior backtracking line search technique projection onto the feasible set. Under some reasonable conditions we establish that close to a regular solution the inexact generalized Newton method is shown to converge locally p-order q-superlinearly. We characterize the order of local convergence based on convergence behavior of the quality of the approximate subdifferentials and indicate how to choose an inexact forcing sequence which preserves the rapid convergence of the proposed algorithm. A nonmonotonic criterion should bring about speeding up the convergence progress in some ill-conditioned cases.     

THE INTERIOR LAYER FOR A NONLINEAR SINGULARLY PERTURBED DIFFERENTIAL-DIFFERENCE EQUATION

In this article,the interior layer for a second order nonlinear singularly perturbed differential-difference equation is considered.Using the methods of boundary function and fractional steps,we constr...