Abstract
The Lyapunov-Schmidt method for bifurcation problems has, until recently, been applied only to operator equations whose singular points are isolated in the solution set of the equation. For bifurcation at a multiple eigenvalue involving several parameters, however, singular points are often non-isolated. In this paper, the case of intersecting curves of singular points is considered. Under natural hypotheses on these curves, and assuming suitable transversality conditions on the first order nonlinearity of the operator, it is shown that the solution set of the equation may be completely determined locally in terms of the solutions of associated finite dimensional polynomial equations.
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Shearer, M. Bifurcation in the neighbourhood of a non-isolated singular point. Israel J. Math. 30, 363–381 (1978). https://doi.org/10.1007/BF02762000
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DOI: https://doi.org/10.1007/BF02762000