Generalised multiparameter simple eigenvalues and bifurcation

Abstract

Let X and Y be Banach spaces and let . Various definitions of the notion of a simple eigenvalue of the multiparameter operator

have appeared in the literature. Here, a generalised definition is proposed which gives rise to eigensurfaces in the parameter space. These eigensurfaces provide points of bifurcation for solutions of the non-linear problem

where N is a nonlinear mapping satisfying some standard conditions.

AMS(MOS)::

• 58E07