Duck solutions, a new kind of bifurcation phenomenon, are discovered and studied during the study of singular perturbation equations in the recent decades.
鸭解是近年来在奇异摄动方程的研究中发现并开始研究的。它是一种新的分支现象。
The existence of periodic solution of singular discrete system is firstly stud - ied and theorem which periodic solutions of singular discrete system exist is given.
首次对广义离散系统的周期解的存在性进行研究，给出了广义离散系统周期解存在的判据。
As an application we utilize the results presented in this paper to study the existence problem of solutions for a class of weakly singular integral equations.
作为所得结果的应用，讨论了弱奇异积分方程解的存在性问题。
First, the general notion of solvability and generalized state solutions for linear discrete coefficient_vary singular systems are analyzed.
首先分析总结了线性离散变系数奇异系统可解性及其广义状态解的一般概念。
By the first integral method, the existence, uniqueness and nonexistence of solutions for some nonlinear ordinary differential equations with singular boundary condition are discussed.
用首次积分法，讨论了带奇异边界条件的非线性常微分方程解的存在性、不存在性和唯一性。
Sufficient and necessary conditions for existence and uniqueness of solutions for initial value problems of singular system are studied in this paper, and the formula of solution is given.
研究了奇异线性系统初值问题解存在唯一的充要条件，并给出了其求解公式。
Some sufficient conditions are given to support the existence of duck solutions and duck cycles when the singular points of the system are in the small neighbourhood of turning points.
给出了当系统的奇点在破坏点的小邻域时鸭解和鸭极限环存在的充分条件。
In this paper, we study the direct method of solution for a class of singular integral equations with solutions having singularities of order one.
本文研究了一类具有一阶奇异性解的完全奇异积分方程的直接解法。
Little attention is on questions of existence of positive solutions for BVP of singular differential equation on measure chains and the relevant papers are few.
测度链上奇异微分方程边值问题正解的存在性，研究的人较少，相应的文献也要少的多。
In chapter 3, we study the energy estimate of singular positive solutions for a class quasilinear elliptic equations.
在第三章中证明了拟线性椭圆型方程正奇异解的能量估计。
This paper discusses the existence of multiple positive solutions of a class of nonlinear singular boundary value problems by means of the fixed point index Theorem on cones.
利用锥映射的不动点指数定理，研究了一类非线性奇异边值问题多个正解的存在性问题。
The main contents are as follows: in chapter 2, we proved that there exists infinitely many singular positive radial solutions which satisfy apriori estimates for quasilinear elliptic equations.
在第二章中我们证明了拟线性椭圆型方程存在无穷多个正奇异对称解，并且满足先验估计。
By using the method of matrix singular values decomposition, the general expressions of the least squares solutions are given.
利用矩阵的奇异值分解和矩阵分块方法，得到了最小二乘解的一般表达式。
The characteristic of this model is: a new interface edge singular element model is derived based on the numerical fundamental solutions obtained from the finite element eigensolutions method.
该模型的独特之处在于：基于有限元特征法得到的奇异性场数值特征解建立了一种新型界面端奇异单元。
According to the type of static singular points, the branching of solutions was determined.
根据静态奇异点的类型计算出解分支。
By using fixed point index theory in a cone, we study the existence of positive solutions of boundary value problems for systems of nonlinear second order singular differential equations.
使用锥上拓扑度理论，研究二阶非线性奇异微分方程组两点边值问题正解的存在性。
By using a direct analysis technique, the existence of nonnegative solutions was established for singular semi-positone problems with p-Laplacian.
用纯分析的方法给出了一类单部件可修系统动态非负解的存在唯一性和单调稳定性证明。
This paper discusses the existence of a class of singular elliptic boundary value problems. Under certain conditions, we prove that weak solutions exist.
讨论了一类具有奇异性的椭圆问题解的存在性。证明了在一定条件下，弱解存在。
The formulas of general solutions and sufficient and necessary conditions of solutions of the initial value problems for a class of singular linear system are studied.
研究了一类奇异线性系统初值问题可解的充要条件及通解公式，给出了奇异线性系统的化简方法及其简单形式，所得结果统一和推广了正常线性系统的相应结。
The author discusses a class of general of singular boundary value problems by using the first integral method, and the necessary and sufficient condition of positive solutions was obtained.
运用首次积分法讨论了较广泛的一类常微分方程边值问题，得到了正解存在的充要条件。
Global existence and uniqueness of solutions is discussed for a class of linear time-varying singular systems with delay.
讨论一类带滞后的线性时变广义系统解的整体存在唯一性问题。
Then, we chose the dispersion number as a characteristic minor parameter, solved the problem and obtained the asymptotic analytical solutions of solute concentration by singular perturbation...
作者选择弥散数作为特征小参数，用奇异摄动法求得了溶质浓度在全流场的渐进解析分布，着重考察了各种因素对浓度前沿推进过程的影响。
Then, we chose the dispersion number as a characteristic minor parameter, solved the problem and obtained the asymptotic analytical solutions of solute concentration by singular perturbation...
作者选择弥散数作为特征小参数，用奇异摄动法求得了溶质浓度在全流场的渐进解析分布，着重考察了各种因素对浓度前沿推进过程的影响。
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