半线性二阶系统的奇异摄动现象<sup>*</sup>

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半线性二阶系统的奇异摄动现象^*

基金项目: * 福建省科学基金资助课题

摘要: 本文研究半线性二阶系统的奇异摄动现象,在适当的假设下,借助于构造特殊的不变域,证得向量边值问题解的存在及其当ε→0⁺时的渐近性质,在这种不变域中解呈现所谓的边界层现象和角层现象.

Abstract: In this paper we consider singular perturbed phenomena of semilinear second ordersystems, under appropriate assumptions, the existence and asymptotic behavior as ε→0⁺ of solution of vector boundary value problem are proved by constructing specialinvariant regions in which solutions display so-called boundary layer phenomena andangular layer phenomena.

[1]	Chang, K.W. and F.A. Howes, Nonlinear Singular Perturbation Phenomena: Theory and Applications, Springer-Verlag, New York, Berlin, Heidelberg, Tokyo (1984).
[2]	O'Malley, R.E., Introduction to Singular Perturbation, Academic Press, New York, London (1974).
[3]	章国华、林宗池,非线性边值的奇摄动,应用数学和力学,5, 5 (1984), 603-612.
[4]	Kelley, W.G., A nonllnear singular perturbation problem for second order systems, SIAM J. Math. Anal., 10, 1 (1979), 32-37.
[5]	Howes. F.A., Singularly perturbed semilinear systems, Studies in Applied Math., 61 (1979), 185-209.
[6]	O'Donnell, M.A., Boundary and corner layer behavior in singularly perturbed semilinear system of boundary value problem, SIAM, J. Math. Anal., 2 (1984).
[7]	章国华、刘光旭,奇摄动半线性系统的边界层和角层性质,应用数学和力学,5, 3 (1984),337-344.
[8]	Chang, K.W. and Lin Zong-chi, Singular perturbation for a class of semilinear second order systems with perturbation both in boundary and in operator, Acta Mathematica Scientia, 5, 2 (1985), 223-241.
[9]	Kelley, W.G., A geometric method of studying two point boundary value problems for second order systems, Rocky Mountain J. Math., 7 (1977), 251-263.

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