Bifurcation of a Continuum of Unstable Modes
In this contribution we consider model equations of increasing complexity which exhibit bifurcation in a continuum of points. In spite of the wealth of solutions present there is - under certain simple geometrical conditions - a selection principle yielding only a finite number of stable solutions. The geometrical conditions mentioned guarantee essentially “supercritical” bifurcation for the continuum as an entity and thus reflect at this level the now classical result for simple eigenvalue bifurcation , .
KeywordsPeriodic Solution Singular Solution Small Solution Simple Eigenvalue Nonzero Solution
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