Local and global bifurcation from normal eigenvalues. II

John Alan MacBain

Vol. 74 (1978), No. 1, 143–152

DOI: 10.2140/pjm.1978.74.143

Abstract

This paper studies the bifurcation of solutions of nonlinear eigenvalue problems of the form Lu = λu + H(λ,u), where L is linear and H is o(∥u∥) uniformly on bounded λ intervals. This paper shows that isolated eigenvalues of L having odd multiplicity are bifurcation points if H merely has a “degree” of compactness, but is not necessarily compact (treated in [3], [5]). Moreover, a global alternative theorem follows.

Mathematical Subject Classification

Primary: 47H15

Milestones

Received: 16 February 1977

Published: 1 January 1978