Vol. 63, No. 2, 1976

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ISSN: 0030-8730
Local and global bifurcation from normal eigenvalues

John Alan MacBain

Vol. 63 (1976), No. 2, 445–466
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) on bounded λ intervals. It is shown that isolated normal eigenvalues of L having odd algebraic multiplicity are bifurcation points, and moreover possess branches of solutions which satisfy an alternative theorem. A related situation is studied, and an application explored.

Mathematical Subject Classification
Primary: 47H15
Milestones
Received: 15 May 1975
Revised: 2 December 1975
Published: 1 April 1976
Authors
John Alan MacBain