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
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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