含两参数的三阶拟线性常微分方程边值问题的奇摄动

Singular Perturbation of Boundary Value Problem for Quasilinear Third Order Ordinary Differential Equations Involving Two Small Parameters

1.
Mathematical Section, Fujian Broadcasting TV University, Fuzhou 350003, P. R. China;
2.
Department of Mathematics, Shanghai Railroad University, Shanghai 200333, P. R. China;
3.
Department of Mathematics, Fujian Normal University, Fuzhou 350007, P. R. China

摘要: 研究含两参数的三阶拟线性常微分方程奇摄动边值问题.采用两阶段展开的方法,对ε/μ²→0(μ→0);μ²/ε→0(ε→0)和ε=μ²三种情形构造出形式渐近解,同时利用微分不等式方法,证明了解的存在性,并给出余项的一致有效的估计.
- 双参数 /
- 奇摄动 /
- 边值问题 /
- 渐近展开
Abstract: The singularly perturbed boundary value problem for quasilinear third order ordinary differential equation involving two small parameters has been considered. For the three cases ε/μ²→0(μ→0);μ²/ε→0(ε→0) and ε=μ², the formal asymptotic solutions are constructed by the method of two steps expansions and the existences of solution are proved by using the differential inequality method. In addition, the uniformly valid estimations of the remainder term are given as well.
- two-parameters /
- singular perturbation /
- boundary value problem /
- asymptotic expansion

[1]	Nayfeh A H.Perturbation Methods[M].New York:Wiley,1973.
[2]	O'Malley R E.Introduction to Singular Perturbations[M].New York:Academic,1974.
[3]	Chang K W,Howes F A.Nonlinear Singular Perturbation Phenomena:Theory and Application[M].New York:Springer-Verlag,1984.
[4]	林宗池,周明儒.应用数学中的摄动方法[M].南京:江苏教育出版社,1995.
[5]	O'Malley R E.Two parameters singular perturbation problems for second order equations[J].J Math Mech,1967,16(10):1143-1163.
[6]	O'Malley R E.Singular perturbations of boundary value problems for linear ordinary differential equations involving two parameters[J].J Math Anal Appl,1967,19:291-309.
[7]	张汉林.关于含双参数的非线性常微分方程的奇摄动[J].应用数学和力学,1989,10(5):453-466.
[8]	苗树梅.具有两个小参数的常微分方程的奇摄动边值问题[J].吉林大学自然科学学报,1991,(4):37-41.
[9]	周雅丽,林宗池.带两参数的三阶非线性微分方程边值问题的奇摄动[J].福建师范大学学报(自然科学版),1997,13(3):13-18.
[10]	Gene A Kleasen.Differential inequalities and existence theorems for second and third order boundary value problems[J].J Differential Equations,1971,10:529-533.

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