Mathematical Proceedings of the Cambridge Philosophical Society

Research Article

Galerkin approximations in several parameter bifurcation problems

J. C. Alexandera1 and P. M. Fitzpatricka1

a1 University of Maryland, Maryland 20742

The purpose of this paper is to prove a theorem giving conditions yielding global bifurcation of the solutions of a family of parameterized nonlinear equations, the domain and the range of which lie in Banach spaces, where the parameter is allowed to be a vector in S0305004100056929_inline1, k a positive integer. The basic contribution is that the parameter is vector valued and that the nonlinearities allowed are very general; however, even for scalar parameters, our results extend those of previous authors.

(Received January 03 1979)