Sequential and continuum bifurcations in degenerate elliptic equations

Authors:
R. E. Beardmore and R. Laister

Journal:
Proc. Amer. Math. Soc. **132** (2004), 165-174

MSC (1991):
Primary 34A09, 34B60, 35B32, 35J60, 35J70

Published electronically:
May 7, 2003

MathSciNet review:
2021259

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Abstract | References | Similar Articles | Additional Information

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

DOI:
https://doi.org/10.1090/S0002-9939-03-06979-X

Keywords:
Degenerate elliptic equations,
sequential and continuum bifurcations,
differential-algebraic equations,
degenerate diffusion

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

Article copyright:
© Copyright 2003
American Mathematical Society