Abstract. The asymptotic behaviour of a solution of the first boundary value problem for a second order elliptic equation is analysed in the case where a small parameter is involved as a factor multiplying only one of the highest order derivatives and the limit equation is an ordinary differential equation. In spite of the fact that the order of the limit equation is the same as that of the original equation, the problem under consideration is bisingular. The asymptotic behaviour of a solution of this problem is analysed using the method of matching asymptotic expansions.

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