Differential Equations and Computational Simulations III
Electron. J. Diff. Eqns., Conf. 01, 1997, pp. 223-235.

Persistence of Crandall-Rabinowitz type bifurcations under small perturbations

Bettina E. Schmidt

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.
Mathematics Subject Classifications: 34B15, 34C23, 46N20.
Key words and phrases: Neumann problem, nonlinear eigenvalue problem, bifurcation from simple eigenvalues, Crandall-Rabinowitz theorem, regular-singular points, perturbed bifurcation theory.

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Bettina E. Schmidt
Department of Mathematics, Auburn University at Montgomery
Montgomery, AL 36124-4023, USA
Email address: bes@strudel.aum.edu
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