Bifurcation from Simple Eigenvalues for Several Parameter Families.

摘要

If lambda = (lambda sub 1,..., lambda sub N) an element of the set R to the nth power, B,A sub 1,..., A sub N are bounded linear operators from a Banach space X to a Banach space Z, the concept of a simple eigenvalue for the operator B - the sum from j = 1 to j = N of lambda sub j A sub j is defined. It is then shown that bifurcation always occurs at simpe eigenvalues and the results are applied to a second order ordinary differential equation with boundary conditions at three distinct points. (Author)