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Discrete Dynamics in Nature and Society
Volume 2008, Article ID 263785, 6 pages
http://dx.doi.org/10.1155/2008/263785
Research Article

Uniqueness and Multiplicity of Solutions for a Second-Order Discrete Boundary Value Problem with a Parameter

1College of Mathematics and Information Science, Shaanxi Normal University, Xian, Shaanxi 710062, China
2Department of Mathematics, Qinghai University for Nationalities, Xining, Qinghai 810007, China

Received 15 November 2007; Accepted 10 February 2008

Academic Editor: Bing-Gen Zhang

Copyright © 2008 Xi-Lan Liu and Jian-Hua Wu. 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. Z. Guo and J. Yu, “Existence of periodic and subharmonic solutions for second-order superlinear difference equations,” Science in China Series A, vol. 46, no. 4, pp. 506–515, 2003. View at Google Scholar · View at MathSciNet
  2. Z. Guo and J. Yu, “The existence of periodic and subharmonic solutions of subquadratic second order difference equations,” Journal of the London Mathematical Society, vol. 68, no. 2, pp. 419–430, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. J. Yu, Z. Guo, and X. Zou, “Periodic solutions of second order self-adjoint difference equations,” Journal of the London Mathematical Society, vol. 71, no. 1, pp. 146–160, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. Z. Guo and J. Yu, “Periodic and subharmonic solutions for superquadratic discrete Hamiltonian systems,” Nonlinear Analysis: Theory, Methods & Applications, vol. 55, no. 7-8, pp. 969–983, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. L. Jiang and Z. Zhou, “Existence of nontrivial solutions for discrete nonlinear two point boundary value problems,” Applied Mathematics and Computation, vol. 180, no. 1, pp. 318–329, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. P. H. Rabinowitz, in Minimax Methods in Critical Point Theory with Applications for Differential Equations, CBMS Regional Conference Series in Mathematics, American Mathematical Society, Providence, RI, USA, 1984. View at Zentralblatt MATH
  7. J. Yu and Z. Guo, “On boundary value problems for a discrete generalized Emden–Fowler equation,” Journal of Differential Equations, vol. 231, no. 1, pp. 18–31, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. J. Yu and Z. Guo, “Boundary value problems of discrete generalized Emden–Fowler equation,” Science in China Series A, vol. 49, no. 10, pp. 1303–1314, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. G. Zhang and S. S. Cheng, “Existence of solutions for a nonlinear system with a parameter,” Journal of Mathematical Analysis and Applications, vol. 314, no. 1, pp. 311–319, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. H. Brezis and L. Nirenberg, “Remarks on finding critical points,” Communications on Pure and Applied Mathematics, vol. 44, no. 8-9, pp. 939–963, 1991. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. T. Gyulov and S. Tersian, “Existence of trivial and nontrivial solutions of a fourth-order ordinary differential equation,” Electronic Journal of Differential Equations, no. 41, pp. 1–14, 2004. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet