Table of Contents Author Guidelines Submit a Manuscript
Abstract and Applied Analysis
Volume 2014, Article ID 175489, 7 pages
http://dx.doi.org/10.1155/2014/175489
Research Article

The Finite Spectrum of Fourth-Order Boundary Value Problems with Transmission Conditions

1Normal College, Hohhot Vocational College, Hohhot 010051, China
2College of Sciences, Inner Mongolia University of Technology, Hohhot 010051, China

Received 15 February 2014; Accepted 4 June 2014; Published 24 June 2014

Academic Editor: Paul W. Eloe

Copyright © 2014 Fang-zhen Bo and Ji-jun Ao. 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. F. V. Atkinson, Discrete and Continuous Boundary Problems, Academic Press, New York, NY, USA, 1964. View at MathSciNet
  2. Q. Kong, H. Wu, and A. Zettl, “Sturm-Liouville problems with finite spectrum,” Journal of Mathematical Analysis and Applications, vol. 263, no. 2, pp. 748–762, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. Q. Kong, H. Volkmer, and A. Zettl, “Matrix representations of Sturm-Liouville problems with finite spectrum,” Results in Mathematics, vol. 54, no. 1-2, pp. 103–116, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. J.-J. Ao, J. Sun, and M.-Z. Zhang, “The finite spectrum of Sturm-Liouville problems with transmission conditions,” Applied Mathematics and Computation, vol. 218, no. 4, pp. 1166–1173, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. J.-J. Ao, J. Sun, and M.-Z. Zhang, “The finite spectrum of Sturm-Liouville problems with transmission conditions and eigenparameter-dependent boundary conditions,” Results in Mathematics, vol. 63, no. 3-4, pp. 1057–1070, 2013. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. J.-J. Ao, J. Sun, and M.-Z. Zhang, “Matrix representations of Sturm-Liouville problems with transmission conditions,” Computers & Mathematics with Applications, vol. 63, no. 8, pp. 1335–1348, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. J.-J. Ao and J. Sun, “Matrix representations of Sturm-Liouville problems with eigenparameter-dependent boundary conditions,” Linear Algebra and Its Applications, vol. 438, no. 5, pp. 2359–2365, 2013. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. J.-J. Ao, J. Sun, and A. Zettl, “Matrix representations of fourth order boundary value problems with finite spectrum,” Linear Algebra and Its Applications, vol. 436, no. 7, pp. 2359–2365, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. J.-J. Ao, J. Sun, and A. Zettl, “Equivalence of fourth order boundary value problems and matrix eigenvalue problems,” Results in Mathematics, vol. 63, no. 1-2, pp. 581–595, 2013. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. J.-J. Ao, F.-Z. Bo, and J. Sun, “Fourth order boundary value problems with finite spectrum,” submitted to Applied Mathematics and Computation.
  11. P. A. Binding, P. J. Browne, and B. A. Watson, “Inverse spectral problems for Sturm-Liouville equations with eigenparameter dependent boundary conditions,” Journal of the London Mathematical Society. Second Series, vol. 62, no. 1, pp. 161–182, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. Z. Akdoğan, M. Demirci, and O. Sh. Mukhtarov, “Green function of discontinuous boundary-value problem with transmission conditions,” Mathematical Methods in the Applied Sciences, vol. 30, no. 14, pp. 1719–1738, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. Q. X. Yang and W. Y. Wang, “A class of fourth order differential operators with transmission conditions,” Iranian Journal of Science and Technology A, vol. 35, no. 4, pp. 323–332, 2011. View at Google Scholar · View at MathSciNet
  14. X.-Y. Zhang and J. Sun, “The determinants of fourth order dissipative operators with transmission conditions,” Journal of Mathematical Analysis and Applications, vol. 410, no. 1, pp. 55–69, 2014. View at Publisher · View at Google Scholar · View at MathSciNet
  15. A. Zettl, Sturm-Liouville Theory, vol. 121 of Mathematical Surveys and Monographs, American Mathematical Society, 2005. View at MathSciNet
  16. W. N. Everitt and D. Race, “On necessary and sufficient conditions for the existence of Carathéodory solutions of ordinary differential equations,” Quaestiones Mathematicae, vol. 2, no. 4, pp. 507–512, 1976. View at Google Scholar · View at MathSciNet
  17. B. Chanane, “Accurate solutions of fourth order Sturm-Liouville problems,” Journal of Computational and Applied Mathematics, vol. 234, no. 10, pp. 3064–3071, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  18. L. Greenberg and M. Marletta, “Numerical methods for higher order Sturm-Liouville problems,” Journal of Computational and Applied Mathematics, vol. 125, no. 1-2, pp. 367–383, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  19. A. Wang, J. Sun, and A. Zettl, “Characterization of domains of self-adjoint ordinary differential operators,” Journal of Differential Equations, vol. 246, no. 4, pp. 1600–1622, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  20. X. Hao, J. Sun, A. Wang, and A. Zettl, “Characterization of domains of self-adjoint ordinary differential operators II,” Results in Mathematics, vol. 61, no. 3-4, pp. 255–281, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet