一类具有三参数的奇摄动方程（II）

本文是〔１〕的继续，指出临界值β￣０时参数和轨线的关系，给出了方程存在鸭环的必要条件。     

一类高阶椭圆型方程奇摄动边值问题

本文讨论了一类２ｍ阶奇摄动椭圆型方程边值问题的渐近性态，得到了问题解的一致有效的渐近展开式。     

极限方程为退缩椭圆型的一类三阶偏微分方程边值问题的奇摄动

本文研究极限方程在部分边界上为椭圆—抛物的一类三阶偏微分方程第一边值问题ε[(?)~3u]/[(?)y~3]-[y(?)~2u]/[(?)x~2]-[(?)~2u]/[(?)y~2]-a(x,y)[(?)u]/[(?)x]-b(x,y)[(?)u]/[(?)y]-c(x,y)u=f(x,y),u|_Γ=0,[(?)u]/[(?)y]|_(y=β)=0的奇摄动,在适当的假设下,证得解的存在并给出任意阶的一致有效的渐近展开式.     

一类具有边界摄动的非线性泛函椭圆型方程奇摄动问题

研究了具有边界摄动的非线性泛函椭圆型方程奇摄动边值问题．在适当的条件下．利用伸长变量、微分不等式理论，讨论了问题解的渐近性态和原问题解的存在唯一性。     

一类具有非局部反应扩散方程的奇摄动问题

本文讨论一类具非局部反应扩散方程的奇摄动初始边值问题，利用迭代法及微分不等式，研究了初始边值问题的存在唯一及其渐近性态。     

一类非线性椭圆型方程奇摄动问题

A class of singularly perturbed problems for the nonlinear elliptic equations is considered. Under suitable conditions, using the theory of differential inequalities the asymptotic behavior of solution for the boundary value problems are studied, which reduced equations possess two intersecting solutions.     

极限方程为椭圆-抛物的四阶椭圆型方程的奇摄动

本文研究了极限方程为椭圆-抛物的四阶椭圆型方程-ε2Δ2u+ym?2u/?y2+?2u/?x2+a(x,y)?u/?y+b(x,y)?u/?x+c(x,y)=0的奇摄动问题,其中ε为正的小参数,m为正的实数,Δ为拉普拉斯算子,a,b,c充分光滑.在适当的假设下,导出可解性的充分条件,证明了解的存在和给出任意阶的一致有效的渐近解.     

一类拟线性椭圆型方程Robin问题的奇摄动

本文研究了一类奇摄动拟线性椭圆型方程Robin问题,在适当的假设下,构造了奇摄动问题的包括边界层的形式渐近解,并利用微分不等式理论证明了所述问题的解的存在性,且给出形式解的一致有效性。     

具有奇性方程的非线性奇摄动问题的正解(英文)

本文讨论了一类具有奇性方程的奇摄动初值问题.在适当条件下,利用微分不等式理论,研究了初值问题解的存在性及其渐近性态,并且得到了具有初始层的一致有效解的渐近展开式.     

两参数非线性发展方程的奇摄动尖层解

本文研究了一类具有非线性发展方程奇摄动问题.引入伸长变量和多重尺度,构造了初始边值问题外部解和尖层、边界层和初始层校正项,得到了问题形式解.利用不动点定理,证明了问题的解的一致有效性.推广了对两参数的奇摄动问题的研究结果.     

SINGULAR PERTURBATION PROBLEMS FOR A CLASS OF ELLIPTIC EQUATIONS OF SECOND ORDER AS DEGENERATED OPERATOR HAS SINGULAR POINTS

In this paper we study the first and tiie third boundary value problems for the elliptic equation \[\begin{array}{l} \varepsilon \left( {\sum\limits_{i,j = 1}^m {{d_{i,j}}(x)\frac{{{\partial ^2}u}}{{\partial {x_i}\partial {x_j}}} + \sum\limits_{i = 1}^m {{d_i}(x)\frac{{\partial u}}{{\partial {x_i}}} + d(x)u} } } \right) + \sum\limits_{i = 1}^m {{a_i}(x)\frac{{\partial u}}{{\partial {x_i}}} + b(x) + c} \ = f(x),x \in G(0 < \varepsilon \le 1), \end{array}\] as the degenerated operator bas singular points, where \[\sum\limits_{i,j = 1}^m {{d_{i,j}}(x){\xi _i}{\xi _j}} \ge {\delta _0}\sum\limits_{i = 1}^m {\xi _i^2} ,({\delta _0} > 0,x \in G).\] The uniformly valid asymptotic solutions of boundary value problems have been obtained under the condition of \[\sum\limits_{i = 1}^m {{a_i}(x){n_i}(x){|_{\partial G}} > 0,or} \sum\limits_{i = 1}^m {{a_i}(x){n_i}(x){|_{\partial G}} < 0} ,\] where \(n = ({n_1}(x),{n_2}(x), \cdots ,{n_m}(x))\) is the interior normal to \({\partial G}\).     

带有集中激励的一类非线性边值问题的奇摄动

本文综合利用近代分析和奇异摄动方法，讨论了一类具有集中激励的非线性向量微分方程组初值总是 的渐近性质，构造了这类问题的一致有效渐近解。并利用这个方法求解几何参数的扁球壳在集中力作用下的非线性稳定性问题，得到了较好的结果。     

一类奇异半线性反应扩散方程初值问题解的存在性

本文获得了如下的奇异半线性反应扩散方程初值问题{(e)u/(e)t-(1/tσ)△u=up+f(x),t＞0,x∈Rnlim t→0+ u (t,x)=0, x∈Rn广义解(mild solution)在L∞ loe[(0,∞);L∞(Rn)]中的存在性.其中σ＞0,0＜p＜1,f(x)非负且f(x)∈L∞(Rn).     

一类双参数奇摄动非线性反应扩散方程

本文研究了一类双参数非线性反应扩散奇摄动问题的模型.利用奇摄动方法,对该问题解的结构在两个小参数相互关联的情形下作了讨论.得到了该问题的渐近解,由解的展开式看出本问题的解同时具有初始层和边界层.     

一类具有高阶奇性解的Hilbert核奇异积分方程

本文利用指数变换研究了一类解具高阶奇性的周期黎曼边值问题,通过转化法研究了一类解具有高阶奇性的Hilber核奇异积分方程,获得了相应的解和可解条件表达式.推广了Hilber核奇异积分方程的结果.     

一类奇异椭圆方程的正解

研究一类奇异椭圆方程问题。利用变分方法和锥理论中的混合单调方法,证明了奇异方程正解的存在性。     

SINGULAR PERTURBATION ON STABILITY FOR A CLASS OF NONLINEAR CONTROL SYSTEMS

1IntroductionStabilitypropertiesofSingularlyperturbedsystemshavebeenstudiedovalthepasttwoorthreede.ade,[1'21.Lyapunovmethodshavebeenwidelyemployed.Themainideaofthispaperistodecompositetheoriginalsystemstotwoseparatesllbsysterns:theso--calledreducedandboun…     

SINGULAR PERTURBATION OF OPTIMAL CONTROL FOR SEMILINEAR INTEGRO-DIFFERENTIAL EQUATIONS

1 IlltroductionWe shall solve a problem Of optimal control consisting of the systemon the interval 0 5 t 5 1, with initial conditionsand the quadratic cost functionalwhich is to be minimized. Here the "T" denotes transposition; I = jot K(t, asx) fi are m-vectors; is gi are n-vectors, u is an r--vector, and the matrix R.is symmetric and positive definite, while the matrices Q and T are symmetricand positive semidefinite throughout 0 5 t S 1 for E > 0 small. fi, g2, 51 and6z are matrix functi…     

A CLASS OF SINGULARLY PERTURBED EQUATIONS FOR LARGE PARAMETER WITH THREE TURNING POINTS

A class of singularly perturbed problem of third order equation with two para-meters is studied. Using singular perturbation method, the structure of solutions to the problem is discussed in three different cases about two small parameters. The asymptotic solutions to the problem are given. The structure of solutions and the different limit behaviors are revealed. And the solutions are compared with the exact solutions to the equation in which the coefficients are constants and a relatively more perfect res...