Sequential and continuum bifurcations in degenerate elliptic equations

Beardmore, R.; Laister, R.

doi:10.1090/S0002-9939-03-06979-X

Sequential and continuum bifurcations in degenerate elliptic equations
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by R. E. Beardmore and R. Laister

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

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

Published electronically: May 7, 2003

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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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