Lin Zong-chi, Lin Su-rong. Interior Layer Phenomena of Semilinear Systems[J]. Applied Mathematics and Mechanics, 1986, 7(3): 197-204.
Citation: Lin Zong-chi, Lin Su-rong. Interior Layer Phenomena of Semilinear Systems[J]. Applied Mathematics and Mechanics, 1986, 7(3): 197-204.

Interior Layer Phenomena of Semilinear Systems

  • Received Date: 1984-07-31
  • Publish Date: 1986-03-15
  • 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.
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  • [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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