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
ID Code:8185
Deposited By: Dr R. Laister
Deposited On:07 Jul 2010 09:25
Last Modified:23 May 2014 20:02

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