具有积分边界条件的二阶半线性奇摄动方程脉冲状对照结构(英文)

本文讨论了带有积分边界条件的二阶半线性奇摄动方程的脉冲状对照结构.借助于边界函数法,在一定条件下,构造了该问题的形式渐近解.利用缝接法证明了该问题解的存在性和形式渐近解的一致有效性.     

一类拟线性奇摄动流体模型的渐近分析

对一类拟线性流体模型进行研究,借助Linard变换将所研究问题转化为可以用边界函数法处理的问题,进而用边界函数法对该方程组进行分析,构造其(n+1)阶形式渐近解,并证明解的存在唯一性和形式渐近解的一致有效性.     

一类拟线性奇异摄动方程组的空间对照结构

本文研究带慢变量的右边不连续的拟线性奇异摄动方程组的空间对照结构.利用边界层函数法构造了该方程组的形式渐近解,并运用"缝接法"证明问题解的存在性以及渐近解的一致有效性.最后,通过例子验证了所得结果的有效性.     

具有快慢层的非光滑奇异摄动问题的空间对照结构

该文研究了具有快慢层的非光滑奇异摄动问题的空间对照结构.利用边界层函数法构造了该问题的形式渐近解,并运用"缝接法"证明了问题光滑解的存在性以及渐近解的一致有效性.最后,通过例子验证了所得结果的有效性.     

二阶非线性奇摄动方程脉冲状空间对照结构

该文对一类二阶非线性奇摄动方程进行研究, 指出该方程在一定条件下可以产生脉冲状空间对照结构, 并用边界函数法构造该问题的渐近解, 证明解的存在性并得到渐近解的误差估计.     

非线性扰动Klein-Gordon方程初值问题的渐近理论

在二维空间中研究一类非线性扰动Klein-Gordon方程初值问题解的渐近理论. 首先利用压缩映象原理,结合一些先验估计式及Bessel函数的收敛性,根据Klein-Gordon方程初值问题的等价积分方程,在二次连续可微空间中得到了初值问题解的适定性;其次,利用扰动方法构造了初值问题的形式近似解,并得到了该形式近似解的渐近合理性;最后给出了所得渐近理论的一个应用,用渐近近似定理分析了一个具体的非线性Klein-Gordon方程初值问题解的渐近近似程度．     

一类带有Neumann边界条件奇异摄动反应扩散方程的周期解

主要研究一类奇异摄动反应扩散方程周期解的存在性和渐近稳定性.首先,利用边界层函数法,构造出形式渐近解,基于微分不等式理论,得到了周期解的存在性.然后讨论周期解在李雅普诺夫意义下的渐近稳定性.最后,由具体例子说明该方法的有效性.     

一个奇摄动微分方程非线性混合边值问题

研究了一个三阶半线性微分方程的奇摄动非线性混合边值问题.利用边界层函数法构造了该问题的形式渐近解,并采用微分不等式理论证明了解的存在性,给出了渐近解的误差估计,最后得出了边界层函数指数型衰减的结论.     

一类分数阶微分方程初值问题的奇摄动

研究了一类非线性分数阶微分方程加权初值问题的奇异摄动.在适当的条件下,首先求出了原问题的外部解,然后利用边界层函数法构造出解的初始层项,并由此得到解的形式渐近展开式,最后利用微分不等式理论,讨论了问题解的渐近性态,得到了原问题解的一致有效的渐近估计式.     

一类具有边界和内部点摄动的非线性问题(英文)

在适当的条件下,用边界摄动理论和微分不等式技巧,研究了一类摄动不仅发生在方程而且同时发生在内部点和边界处的非线性奇摄动问题.利用改进以往相关文献中辅助函数的构造证明了解的存在性,得到了原问题解以及解的导函数的任意阶一致有效渐近表达式.本文的结果丰富和推广了相关成果.     

一类四阶非线性奇摄动方程的边值问题

利用匹配渐近展开法,讨论了一类四阶非线性方程的具有两个边界层的奇摄动边值问题．引进伸长变量,根据边界条件与匹配原则,在一定的可解性条件下,给出了外部解和左右边界层附近的内层解,得到了该问题的二阶渐近解,并举例说明了这类非线性问题渐近解的存在性．     

THE SOLVABILITY FOR NONLINEAR SINGULARLY PERTURBED DIFFERENTIAL SYSTEM

The solvability for the nonlinear singularly perturbed boundary value pro- blem of differential system is considered.Using the boundary layer corrective method the formal asymptotic solution is constructed.And using the theory of differential inequality proves the uniform validity of the asymptotic expansion for the solution.     

SOLVABILITY OF SOME SINGULARLY PERTURBED SEMI-LINEAR DIFFERENTIAL SYSTEM

In this paper, we consider the solvability for a singularly perturbed Robin problem of semi-linear differential system. Using the boundary layer corrective method, the formal asymptotic solution is constructed. Finally, the uniform validity of such asymptotic expansions solution is proved.     

THE SOLVABILITY FOR A CLASS OF SINGULARLY PERTURBED QUASI-LINEAR DIFFERENTIAL SYSTEM

The solvability for a class of singularly perturbed Robin problem of quasilinear differential system is considered. Using the boundary layer corrective method the formal asymptotic solution is constructed. And using the theory of differential inequality the uniform validity of the asymptotic expansions for solution is proved.     

The nonlinear nonlocal singularly perturbed problems for reaction diffusion equations with a boundary perturbation

The nonlinear nonlocal singularly perturbed initial boundary value problems for reaction diffusion equations with a boundary perturbation is considered. Under suitable conditions, the outer solution of the original problem is obtained. Using the stretched variable, the composing expansion method and the expanding theory of power series the initial layer is constructed. And then using the theory of differential inequalities the asymptotic behavior of solution for the initial boundary value problems is studied. Finally the existence and uniqueness of solution for the original problem and the uniformly valid asymptotic estimation are discussed.     

一类非线性奇摄动系统的可解性及渐近解

研究了一类非线性微分系统的奇摄动边值问题.利用边界层校正法构造了形式渐近解和用微分不等式理论,证明了解的渐近展开式的一致有效性,得到了相应的定理,从而得到了原问题的可解性条件.     

具非线性边界条件的半线性时滞微分方程边值问题奇摄动

利用微分不等式理论研究了一类具非线性边界条件的半线性时滞微分方程边值问题.采用新的方法构造上下解,得到了此边值问题解的存在性的充分条件,并给出了解的一致有效渐近展开式.     

The interior layer phenomena for a class of singularly perturbed delay-differential equations

In this article, we study a kind of vector singularly perturbed delay-differential equation. Using boundary layer function method and geometric analysis skill, the asymptotic expression of the system is constructed and the uniform validity of asymptotic solution is also proved.     

The singular perturbation of boundary value problem for third-order nonlinear vector integro-differential equation and its application

In this paper, the singular perturbation of boundary value problem to a class of third-order nonlinear vector integro-differential equation is studied. Using the method of differential inequalities, under certain conditions, the existence of perturbed solution is proved, the uniformly valid asymptotic expansion for arbitrary order and the estimation of remainder term are given. Finally, the results are applied to study singularly perturbed boundary value problem to a nonlinear vector fourth-order differential equation. The existence of solution and its asymptotic estimation can be obtained conveniently.