Sequential and continuum bifurcations in degenerate elliptic equations

Beardmore, R. E. and Laister , R. (2004) Sequential and continuum bifurcations in degenerate elliptic equations. Proceedings of the American Mathematical Society, 132 (01). pp. 165-174. ISSN 0002-9939

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Publisher's URL: http://dx.doi.org/10.1090/S0002-9939-03-06979-X

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.

Item Type:Article
Uncontrolled Keywords:degenerate elliptic equations, sequential and continuum bifurcations, differential-algebraic equations, degenerate diffusion
Faculty/Department:Faculty of Environment and Technology > Department of Engineering Design and Mathematics
~Pre-2010 Faculty Structure > Environment and Technology > Bristol Institute of Technology > Applied Mathematics Group
~Pre-2012 Faculty Structure > Faculty of Environment and Technology > Department of Engineering Design and Mathematics
ID Code:8185
Deposited By: Dr R. Laister
Deposited On:07 Jul 2010 09:25
Last Modified:25 Nov 2012 17:50

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