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Sequential and continuum bifurcations in degenerate elliptic equations
Author(s):
R.
E.
Beardmore;
R.
Laister
Journal:
Proc. Amer. Math. Soc.
132
(2004),
165-174.
MSC (1991):
Primary 34A09, 34B60, 35B32, 35J60, 35J70
Posted:
May 7, 2003
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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:
10.1090/S0002-9939-03-06979-X
PII:
S 0002-9939(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
Posted:
May 7, 2003
Communicated by:
Carmen C. Chicone
Copyright of article:
Copyright
2003,
American Mathematical Society
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