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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Sequential and continuum bifurcations in degenerate elliptic equations
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by R. E. Beardmore and R. Laister PDF
Proc. Amer. Math. Soc. 132 (2004), 165-174 Request permission

Abstract:

We examine the bifurcations to positive and sign-changing solutions of degenerate elliptic equations. In the problems we study, which do not represent Fredholm operators, we show that there is a critical parameter value at which an infinity of bifurcations occur from the trivial solution. Moreover, a bifurcation occurs at each point in some unbounded interval in parameter space. We apply our results to non-monotone eigenvalue problems, degenerate semi-linear elliptic equations, boundary value differential-algebraic equations and fully non-linear elliptic equations.
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Additional Information
  • R. E. Beardmore
  • Affiliation: Department of Mathematics, Imperial College, South Kensington, London, SW7 2AZ, United Kingdom
  • Email: r.beardmore@ic.ac.uk
  • R. Laister
  • Affiliation: Department of Mathematics, University of the West of England, Frenchay Campus, Bristol, United Kingdom
  • Email: robert.laister@uwe.ac.uk
  • Received by editor(s): May 13, 2002
  • Received by editor(s) in revised form: August 21, 2002
  • Published electronically: May 7, 2003
  • Communicated by: Carmen C. Chicone
  • © Copyright 2003 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 132 (2004), 165-174
  • MSC (1991): Primary 34A09, 34B60, 35B32, 35J60, 35J70
  • DOI: https://doi.org/10.1090/S0002-9939-03-06979-X
  • MathSciNet review: 2021259