About this Journal Submit a Manuscript Table of Contents
Abstract and Applied Analysis
Volume 2012 (2012), Article ID 804619, 8 pages
http://dx.doi.org/10.1155/2012/804619
Research Article

Global Bifurcation in -Order Generic Systems of Nonlinear Boundary Value Problems

College of Mathematics and Statistics, Northwest Normal University, Lanzhou, Gansu 730070, China

Received 17 September 2012; Accepted 23 November 2012

Academic Editor: Chuandong Li

Copyright © 2012 Xiaoling Han et al. 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.

Linked References

  1. B. P. Rynne, “Global bifurcation in generic systems of nonlinear Sturm-Liouville problems,” Proceedings of the American Mathematical Society, vol. 127, no. 1, pp. 155–165, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  2. R. S. Cantrell, “Multiparameter bifurcation problems and topological degree,” Journal of Differential Equations, vol. 52, no. 1, pp. 39–51, 1984. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  3. U. Elias, “Eigenvalue problems for the equations Ly+λp(x)y=0,” Journal of Differential Equations, vol. 29, no. 1, pp. 28–57, 1978. View at Publisher · View at Google Scholar
  4. J. C. Saut and R. Temam, “Generic properties of nonlinear boundary value problems,” Communications in Partial Differential Equations, vol. 4, no. 3, pp. 293–319, 1979. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  5. P. Brunovský and P. Poláčik, “The Morse-Smale structure of a generic reaction-diffusion equation in higher space dimension,” Journal of Differential Equations, vol. 135, no. 1, pp. 129–181, 1997. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  6. A. E. Taylor and D. C. Lay, Introduction to Functional Analysis, John Wiley & Sons, 2nd edition, 1980.
  7. B. P. Rynne, “The structure of Rabinowitz' global bifurcating continua for generic quasilinear elliptic equations,” Nonlinear Analysis: Theory, Methods & Applications, vol. 32, no. 2, pp. 167–181, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  8. E. Zeidler, Nonlinear Functional Analysis and Its Applications. I, Springer, 1986. View at Publisher · View at Google Scholar
  9. X. L. Han and R. L. An, “A generic result for an eigenvalue problem with indefinite weight function,” Acta Mathematica Sinica, vol. 53, no. 6, pp. 1111–1118, 2010. View at Zentralblatt MATH
  10. R. Ma and X. Han, “Existence of nodal solutions of a nonlinear eigenvalue problem with indefinite weight function,” Nonlinear Analysis: Theory, Methods & Applications, vol. 71, no. 5-6, pp. 2119–2125, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  11. R. Ma and X. Han, “Existence and multiplicity of positive solutions of a nonlinear eigenvalue problem with indefinite weight function,” Applied Mathematics and Computation, vol. 215, no. 3, pp. 1077–1083, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  12. J. Xu and X. Han, “Existence of nodal solutions for Lidstone eigenvalue problems,” Nonlinear Analysis: Theory, Methods & Applications, vol. 67, no. 12, pp. 3350–3356, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH