Abstract and Applied Analysis
Volume 2011 (2011), Article ID 302942, 11 pages
http://dx.doi.org/10.1155/2011/302942
Research Article

A Fold Bifurcation Theorem of Degenerate Solutions in a Perturbed Nonlinear Equation

Ping Liu and Yuwen Wang

Y.Y. Tseng Functional Analysis Research Center and School of Mathematical Sciences, Harbin Normal University, Harbin, Heilongjiang, 150025, China

Received 21 January 2011; Revised 29 March 2011; Accepted 6 May 2011

Academic Editor: Stefan Siegmund

Copyright © 2011 Ping Liu and Yuwen Wang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We consider a nonlinear equation F(ε,λ,u)=0, where the parameter ε is a perturbation parameter, F is a differentiable mapping from R×R×X to Y, and X, Y are Banach spaces. We obtain an abstract bifurcation theorem by using the generalized saddle-node bifurcation theorem.