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刘其林 《高校应用数学学报(A辑)》1993,(3):231-238
本文研究一类非线性微分方程的非线性边值问题的奇摄动,应用边界层校正法构造出解的形式渐近展开式,并借助于上,下解及微分不等式理论研究解及其一阶导数的有关余项估计。 相似文献
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研究了一类奇摄动非线性分数阶微分方程边值问题.在适当的条件下,首先求出了原问题的外部解,然后利用伸长变量、合成展开法和幂级数展开理论构造出解的边界层项,并由此得到解的渐近展开式.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. 相似文献
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关于三阶非线性奇摄动边值问题的研究,近年来,国内外学者做过一些研究。然而,关于这类问题解的唯一性问题,则仅仅在文献[4]、[5]中作过某些讨论。本文所要讨论的微分方程具有一种奇异特性,亦即fx″(t,x,x′,ε)≡0。而且当ε=0时三阶边值问题退化为一阶初值问题。所有这些特点,无疑将给对边值问 相似文献
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奇摄动非线性边值问题 总被引:1,自引:0,他引:1
本文研究了奇摄动非线性边值问题(?)其中y,f,A,B为n-维向量.在适当的假设下作者利用微分不等式方法证明了存在一个解y(x,ε) ,并得到了它的估计式. 相似文献
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唐荣荣 《数学物理学报(A辑)》2008,28(6):1128-1132
利用渐近理论和微分不等式的方法,该文研究了一类非线性奇摄动Robin问题. 证明了其解的存在性,并得到了解的任意n 阶一致有效渐近展开式. 相似文献
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三阶非线性边值问题的奇摄动 总被引:1,自引:0,他引:1
本文利用Volterra型积分算子和微分不等式技巧给出了一类三阶非线性微分方程奇摄动边值问题:εx=f(t,x,ε),x(0)=A,g(x’(0),x‘(0),ε)=0,h(x(1),x(1),ε)=0解的存在性,唯一性及渐近估计。 相似文献
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Ouyang Cheng Mo Jiaqi 《Annals of Differential Equations》2005,21(2):177-182
The nonlinear singularly perturbed problems for reaction diffusion equations with boundary perturbation are considered. Under suitable conditions, using the theory of differential inequalities the asymptotic behavior of solution for the initial boundary value problems is studied. 相似文献
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莫嘉琪 《数学物理学报(B辑英文版)》2003,23(3)
A class of nonlinear singularly perturbed problems for reaction diffusion equa-tions are considered. Under suitable conditions, by using the theory of differential inequal-ities, the asymptotic behavior of solutions for the initial boundary value problems arestudied, reduced problems of which possess two intersecting solutions. 相似文献
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A CLASS OF NONLINEAR PREDATOR-PREY SINGULARLY PERTURBED ROBIN PROBLEMS FOR REACTION DIFFUSION SYSTEM
A class of nonlinear predator-prey singularly perturbed Robin problems for reaction diffusion systems are considered. Under suitable conditions, using the theory of differential inequalities the existence and asymptotic behavior of solution for the initial boundary value problems are studied. 相似文献
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本文是讨论一类在局部区域上的奇摄动非线性Robin边值问题。利用算子理论和不动点原理,得到了相应问题解的存在性和唯一性。 相似文献
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ASYMPTOTIC SOLUTION FOR A CLASS OF WEAKLY NONLINEAR SINGULARLY PERTURBED REACTION DIFFUSION EQUATION
Mo Jiaqi 《Annals of Differential Equations》2006,22(4):535-539
In this paper a class of nonlinear reaction diffusion problems are considered. Using the perturbed method, the asymptotic solution for corresponding problem is obtained. 相似文献
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莫嘉琪 《Annals of Differential Equations》2004,20(4):396-401
A class of nonlinear nonlocal singularly perturbed boundary value problems for elliptic equation with boundary perturbation is considered. Under suitable conditions, firstly, the outer solution of the original problem is obtained, secondly, using the stretched variable, the composing expansion method and the expanding theory of power series, the boundary layer is constructed, finally, using the theory of differential inequalities the asymptotic behavior of solution for the boundary value problems is studied and educing some relational inequalities the existence and uniqueness of solution for the original problem and the uniformly valid asymptotic estimation is discussed. 相似文献
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§ 1 IntroductionA class of singularly perturbed boundary value problems were studied by Mo[1~ 6] .Now we consider the following singularly perturbed nonlinear boundary value problem ofthe formεd2 ydx2 =f(x,y,y′) , 0 相似文献
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一类非线性奇摄动系统的可解性及渐近解 总被引:1,自引:0,他引:1
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. 相似文献