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Sequential and continuum bifurcations in degenerate elliptic equations

Beardmore, R. E.; Laister, Robert


R. E. Beardmore


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.


Laister, R., Beardmore, R. E., & Laister, R. (2004). Sequential and continuum bifurcations in degenerate elliptic equations. Proceedings of the American Mathematical Society, 132(01), 165-174.

Journal Article Type Conference Paper
Publication Date Jan 1, 2004
Journal Proceedings of the American Mathematical Society
Print ISSN 0002-9939
Publisher American Mathematical Society
Peer Reviewed Peer Reviewed
Volume 132
Issue 01
Pages 165-174
Keywords degenerate elliptic equations, sequential and continuum bifurcations, differential-algebraic equations, degenerate diffusion
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