Interior Layer Phenomena of Semilinear Systems

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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.

Citation:

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

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.

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