- About this Journal ·
- Abstracting and Indexing ·
- Aims and Scope ·
- Annual Issues ·
- Article Processing Charges ·
- Articles in Press ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
Abstract and Applied Analysis
Volume 2012 (2012), Article ID 804619, 8 pages
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.
- 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.
- R. S. Cantrell, “Multiparameter bifurcation problems and topological degree,” Journal of Differential Equations, vol. 52, no. 1, pp. 39–51, 1984.
- U. Elias, “Eigenvalue problems for the equations ,” Journal of Differential Equations, vol. 29, no. 1, pp. 28–57, 1978.
- 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.
- 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.
- A. E. Taylor and D. C. Lay, Introduction to Functional Analysis, John Wiley & Sons, 2nd edition, 1980.
- 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.
- E. Zeidler, Nonlinear Functional Analysis and Its Applications. I, Springer, 1986.
- 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.
- 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.
- 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.
- 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.