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.