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Zeitschrift für Analysis und ihre Anwendungen


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Volume 1, Issue 5, 1982, pp. 1–15
DOI: 10.4171/ZAA/32

Published online: 1982-10-31

Die Methode der Grenzschichtverbesserung für eine Masse entarteter gewöhnlicher Differentialgleichungen

Sybille Meyer[1]

(1) Technische Universität Chemnitz, Germany

In this paper we generalize Visik’s and Ljusternik’s method for a symptotic solution of boundary value problems with a small parameter in the highest derivatives of the differential equation for a class of boundary value problems for non-self-adjoint ordinary differential equations of the order $2m$, in which the coefficients have a zero of integer order in a boundary point. A part of the arising boundary layer equations having singularities. In Chapter 3 of this paper we calculate the index of the differential operators of this boundary layer equations in a certain pair of spaces of the positive half-axis. In Chapter 4 we construct the first term of an asymptotic solition for small parameter values.

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Meyer Sybille: Die Methode der Grenzschichtverbesserung für eine Masse entarteter gewöhnlicher Differentialgleichungen. Z. Anal. Anwend. 1 (1982), 1-15. doi: 10.4171/ZAA/32