About this Journal Submit a Manuscript Table of Contents
Abstract and Applied Analysis
Volume 2012 (2012), Article ID 753857, 16 pages
http://dx.doi.org/10.1155/2012/753857
Research Article

Asymptotic Behavior of Bifurcation Curve for Sine-Gordon-Type Differential Equation

Laboratory of Mathematics, Institute of Engineering, Hiroshima University, Higashi-Hiroshima 739-8527, Japan

Received 23 October 2012; Accepted 11 December 2012

Academic Editor: Sining Zheng

Copyright © 2012 Tetsutaro Shibata. 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. Y. Kamimura, “An inverse problem in bifurcation theory,” Journal of Differential Equations, vol. 106, no. 1, pp. 10–26, 1993. View at Publisher · View at Google Scholar · View at MathSciNet
  2. R. Benguria and M. C. Depassier, “Upper and lower bounds for eigenvalues of nonlinear elliptic equations. I. The lowest eigenvalue,” Journal of Mathematical Physics, vol. 24, no. 3, pp. 501–503, 1983. View at Publisher · View at Google Scholar · View at MathSciNet
  3. H. Berestycki, “Le nombre de solutions de certains problèmes semi-linéaires elliptiques,” Journal of Functional Analysis, vol. 40, no. 1, pp. 1–29, 1981. View at Publisher · View at Google Scholar · View at MathSciNet
  4. S. Cano-Casanova and J. López-Gómezb, “Existence, uniqueness and blow-up rate of large solutions for a canonical class of one-dimensional problems on the half-line,” Journal of Differential Equations, vol. 244, no. 12, pp. 3180–3203, 2008. View at Publisher · View at Google Scholar · View at MathSciNet
  5. S. Cano-Casanova and J. López-Gómezb, “Blow-up rates of radially symmetric large solutions,” Journal of Mathematical Analysis and Applications, vol. 352, no. 1, pp. 166–174, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  6. J. M. Fraile, J. López-Gómezb, and J. C. Sabina de Lis, “On the global structure of the set of positive solutions of some semilinear elliptic boundary value problems,” Journal of Differential Equations, vol. 123, no. 1, pp. 180–212, 1995. View at Publisher · View at Google Scholar · View at MathSciNet
  7. T. Shibata, “Global behavior of the branch of positive solutions to a logistic equation of population dynamics,” Proceedings of the American Mathematical Society, vol. 136, no. 7, pp. 2547–2554, 2008. View at Publisher · View at Google Scholar · View at MathSciNet
  8. M. G. Crandall and P. H. Rabinowitz, “Bifurcation from simple eigenvalues,” Journal of Functional Analysis, vol. 8, pp. 321–340, 1971. View at MathSciNet
  9. T. Shibata, “Precise spectral asymptotics for nonlinear Sturm-Liouville problems,” Journal of Differential Equations, vol. 180, no. 2, pp. 374–394, 2002. View at Publisher · View at Google Scholar · View at MathSciNet
  10. T. Shibata, “Variational method for precise asymptotic formulas for nonlinear eigenvalue problems,” Results in Mathematics, vol. 46, no. 1-2, pp. 130–145, 2004. View at MathSciNet
  11. T. Shibata, “Local structure of bifurcation curves for nonlinear Sturm-Liouville problems,” Journal of Mathematical Analysis and Applications, vol. 369, no. 2, pp. 583–594, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  12. I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products, Academic Press, San Diego, Calif, USA, 5th edition, 1994. View at MathSciNet
  13. T. Shibata, “Asymptotic properties of variational eigenvalues for semilinear elliptic operators,” Unione Matematica Italiana, vol. 7, no. 2, pp. 411–425, 1988. View at MathSciNet