半线性系统的内层现象

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Interior Layer Phenomena of Semilinear Systems

摘要: 本文研究半线性系统
εy″=f(t,y,ε) (ay(a,ε)=A(ε), y(b,ε)=B(ε)
的奇摄动边值问题的内层现象,其中ε>0是一个小参数,y、f、A和B是n-维向量函数。这种向量边值问题似乎还没有研究过,尽管纯量的边值问题已广泛地研究过。在适当地假设下如同纯量问题一样我们得到解的存在、同时使用适当的不等式,这个解的估计也得到。

Abstract: In this paper, we study the interior layer phenomena of singular perturbation boun-dary value problems for semilinear systems:
εy″=f(t,y,ε) (ay(a,ε)=A(ε), y(b,ε)=B(ε)
where ε>0 is a small parameter, y, f, A and B arc n-dimensional vector functions, This vector boundary value problem does not appear to have been studied, although the scalar boundary problem has been treated extensively, Under appropriate assumptions we obtain existence of solution as in the scalar problem and the estimate of this solution in terms of appropriate inequalities as well.

[1]	Chang, K, W, and F,A, Howes, Nonlinear Singular Perlurbotion Phenomena, Springer-Yerlag Pub, (in press).
[2]	Bernfeld, S, and Y, Lakshmikantham, An Introduction to Nonlinear Boundary Value Problems, Academic Press, New York (1974).
[3]	Hebets.P, and M. Laloy, Etude de problems aua limites par la method des sur-et sous-solution, Lecture notes, Catholic University of Louvain (1974).
[4]	Chang, K, W, and G, X, Liu, Boundary and angular layer behavior in singularly perturbed semilinear systems, Appl,Math, and Nlech, 5, 3 (1984),1309-1316.
[5]	林宗池,一类半线性系统一奇摄动边值问题解的估计(待发表).

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