Non-Linear Sturm-Liouville Problems with No Secondary Bifurcation.

Abstract

The paper is concerned with giving sufficient conditions that in the non-linear boundary-value problem u'(x) + (q(x) + G(x,u(x), lambda))u(x) = 0 with u(0) = 0, u(1) = 0 or u'(1) = 0 there should be no secondary bifurcation, i.e. that, given a branch of solutions (u, lambda) bifurcating from the trivial solution, there should be no further bifurcation on that branch. Sufficient conditions on G are given which include, for example, Kolodner's problem of the motion of a heavy rotating string. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Sep 01, 1977
Accession Number
ADA049399

Entities

People

  • C. A. Stuart
  • J. B. Mcleod

Organizations

  • University of Wisconsin–Madison

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  • C4I

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  • Banach Space
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  • Boundary Value Problems
  • Buckling
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  • Formulas (Mathematics)
  • Inequalities
  • Integral Equations
  • Intervals
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  • United States

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  • Mathematics

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