A Complete Analysis of a Model Nonlinear Singular Perturbation Problem Having a Continuous Locus of Singular Points.

Abstract

Consider the boundary value problem epsilon y double prime = (y sq - t sq) y', -1 < t < 0, y(-1) = A, y(0) = B. Depending on the choice of A and B, one can insure the existence of 'turning points'. However, due to the nonlinear nature of the problem, one does not know the position or number of such turning points. In the case when A > 0 = B Kedem, Parter and Steuerwalt gave a development of this problem based on an abstract bifurcation analysis which in turn was based on 'degree theory'. In this paper we give a complete analysis of the problem based entirely on a -priori estimates and the 'shooting' method.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1981
Accession Number
ADA096323

Entities

People

  • Nancy Kopell
  • Seymour V. Parter

Organizations

  • University of Wisconsin Madison Department of Computer Science

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  • Mathematics

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