Electronic Journal of Differential Equations,
Conference 01 (1998), pp. 223-235.

Title: Persistence of Crandall-Rabinowitz type bifurcations 
       under small perturbations

Author: Bettina E. Schmidt (Auburn Univ., Montgomery, AL, USA)
 
Abstract: 
We discuss a class of nonlinear operator equations in a Banach space 
setting and present a generalization of the Crandall-Rabinowitz 
bifurcation theorem that describes the effect of small perturbations 
of the operators involved on the local structure of the solution 
set in the vicinity of a bifurcation point of the unperturbed equation.
 The result is applied to a parameter-dependent Neumann boundary-value 
problem with spatially homogeneous source terms that exhibits 
infinitely many bifurcation points. We obtain conditions for the 
persistence or nonpersistence of these bifurcations under small, 
spatially inhomogeneous perturbations of the source terms.

Published November 12, 1998.
Math Subject Classifications: 34B15, 34C23, 46N20.
Key Words: Neumann problem; nonlinear eigenvalue problem;
bifurcation from simple eigenvalues; Crandall-Rabinowitz theorem; 
regular-singular points; perturbed bifurcation theory.