Sequential and continuum bifurcations in degenerate elliptic equations

Beardmore, R. E.; Laister, Robert

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.

• Journal Article Type: Article
• Online Publication Date: May 7, 2003
• Publication Date: Jan 1, 2004
• Deposit Date: Jul 7, 2010
• Publicly Available Date: Mar 19, 2016
• Journal: Proceedings of the American Mathematical Society
• Print ISSN: 0002-9939
• Electronic ISSN: 1088-6826
• Peer Reviewed: Peer Reviewed
• Volume: 132
• Issue: 01
• Pages: 165-174
• DOI: https://doi.org/10.1090/S0002-9939-03-06979-X
• Keywords: degenerate elliptic equations, sequential and continuum bifurcations, differential-algebraic equations, degenerate diffusion
• Public URL: https://uwe-repository.worktribe.com/output/1064230
• Publisher URL: http://dx.doi.org/10.1090/S0002-9939-03-06979-X
• Contract Date: Mar 19, 2016