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1.
BOUNDARY VALUE PROBLEMS TO A CLASS OF SINGULARLY PERTURBED NONLINEAR SYSTEM WITH TURNING POINTS 总被引:1,自引:0,他引:1
ConsidertheboundaryvalueproblemtothesingularlyperturbednonlinearsystemintheformofwhereEisasmallpositiveparameter,y=(yi,'..)y.),f=(fi,...)fn),A=(Al,'',A.)andB=(BI,sn).MohasdiscussedtheseDroblemsundervarioussituationsusingthemethodofdifferentialinequalities[1--'].Inthispaperweconsiderthecaseoffi.:(0,y,y')=0anduseaclassofnewboundarylayerfunctions.TheoremAssumethat(a)fi(x,y,z)Hfi(x,yi,'',yn,if)''jz.)eC'{xE[~l,1],yie[di,ei],ifER}andtherearepositivenondecreasingcontinuousfunctionsif,i=1,2,'… 相似文献
2.
§ 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
3.
拟线性积分微分方程系统的奇摄动边值问题 总被引:5,自引:0,他引:5
本文研究高维拟线性积分微分方程系统边值问题的奇摄动,在适当的条件下,利 用渐近分析方法和对角化技巧,证得解的存在性,同时给出解的渐近展开式及其相应的 余项估计. 相似文献
4.
非线性积分微分方程组奇摄动边值问题 总被引:2,自引:0,他引:2
本文讨论含积分算子的非线性微分方程组Robin边值问题的奇摄动,在适当假设条件下通过对角化技巧,利用逐步逼近法证明了解的存在,并得到直到O(ε^N+1)的按范数界限的一致有效估计。 相似文献
5.
§ 1 IntroductionSince 1 970 the perturbed boundary value problems for functional differential equationshave been derived in many fields,such as biology,physics,optimal control and e-conomies[1 ] .Some works on studying it have appeared,for example references[2~ 6] .Inthis paper,we study a kind of singularly perturbed boundary value problems for Volterrafunctional differential equations:εx″(t) =f(t,x(t) ,[Tx] (t) ,x(t-τ) ,x′(t) ,ε) ,t∈ (0 ,1 ) ,(1 )x(t) =φ(t,ε) ,t∈ [-τ,0 ] ,ax(1 )… 相似文献
6.
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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8.
谢峰 《Annals of Differential Equations》2002,(4)
In this paper, a class of singular perturbation of boundary value problem for nonlinear second order ordinary differential equation involving two parameters is considered. For the three cases ε/μ→0(μ→0), μ2/ε→0(ε→0) and ε=μ2, uniformly valid asymptotic solutions are obtained using the method of two steps expansions and a fixed-point theorem. 相似文献
9.
Considerasingularlyperturbedproblemforhigherorderselnilinearequationswhereeisasmallpositiveparameter,ndenotesaboundedregioninRe,whereonsignifiesasmoothboundaryofn,misaintegerandjk,gi,k,j=0,'',in--1,aresufficientlysmoothfunctionswithregardtotheirvariablesincorrespondenceranges.Modealwiththesingularperturbationforthesecondorder'ellipticequations[1],[2],thefourthorderequations[3]l[4]andaclassofhigherorderequations[5].Inthispaperttheauthorsconsiderthesingularperturbationforevenmoregeneralhigheror… 相似文献
10.
Yao Jingsun~ Chen Lihua~ Mo Jiaqi~ 《Annals of Differential Equations》2007,23(3):358-364
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. 相似文献
11.
1IntroductionSince1970,theboundaryvalueproblemsforfunctionaldiferentialequationhavebenderivativedfrommanyfields,suchasbiology... 相似文献
12.
Chen Xiu 《Annals of Differential Equations》2007,23(2):131-135
In this paper,we study the singular perturbation of boundary value problem for a class of n-th order nonlinear differential equation,the solution is shown to exhibit multiple layer behavior.According to different layers and by introducing extended variable,we obtain the uniformly effective asymptotic expansion with different boundary layer correction term. 相似文献
13.
《数学物理学报(B辑英文版)》1999,19(5):589-597
This paper investigates the boundary value problems for a class of singularly perturbed nonlinear elliptic equations. By means of the theory of partial differential inequalities the author obtains the existence and asymptotic estimation of the solutions, involving the boundary and interior layer behavior, of the problems as described. 相似文献
14.
奇摄动非线性系统初值问题的套层解 总被引:8,自引:0,他引:8
本文研究一类二阶非线性系统的初值问题的奇摄动,揭示了其解呈现双重初始层的性质,通过引进不同量级的伸长变量,得到解的一致有效的渐近展开式。 相似文献
15.
Zhou Mingru 《Annals of Differential Equations》2005,21(4):639-647
This paper is concerned with boundary and corner layer behavior of the singularly perturbed Robin boundary value problem(RP) for the second-order nonlinear differential equations. The existence and asymptotic estimate of solutions of (RP) is discussed by appropriately constructing the bounding functions and using the theory of differential inequality. 相似文献
16.
In this paper the singularly perturbed initial boundary value problems for the nonlocal reaction diffusion system are considered. Unsing the iteration method and the comparison theorem, the existence, uniqueness and its asymptotic behavior of solution for the problem are studied. 相似文献
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18.
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
19.
本文研究了催化反应非线性奇摄动边值问题.利用微分不等式理论和方法,得到了问题的解的任意次近似渐近估计. 相似文献