Sequential and continuum bifurcations in degenerate elliptic equations |
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Authors: | R. E. Beardmore R. Laister |
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Affiliation: | Department of Mathematics, Imperial College, South Kensington, London, SW7 2AZ, United Kingdom ; Department of Mathematics, University of the West of England, Frenchay Campus, Bristol, United Kingdom |
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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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Keywords: | Degenerate elliptic equations sequential and continuum bifurcations differential-algebraic equations degenerate diffusion |
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