Sequential and continuum bifurcations in degenerate elliptic equations
Beardmore, R. E. and Laister, R.
Sequential and continuum bifurcations in degenerate elliptic equations.
Proceedings of the American Mathematical Society, 132 (01).
Available from: http://eprints.uwe.ac.uk/8185
- Published Version
Publisher's URL: http://dx.doi.org/10.1090/S0002-9939-03-06979-X
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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