Table of Contents Author Guidelines Submit a Manuscript
Discrete Dynamics in Nature and Society
Volume 2009, Article ID 407623, 14 pages
http://dx.doi.org/10.1155/2009/407623
Research Article

Existence of Solutions to Boundary Value Problems for the Discrete Generalized Emden-Fowler Equation

Department of Computation Science, Zhongkai University of Agriculture and Engineering, Guangzhou, Guangdong 510225, China

Received 16 May 2009; Revised 30 October 2009; Accepted 29 November 2009

Academic Editor: Leonid Berezansky

Copyright © 2009 Tieshan He and Fengjian Yang. 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. R. P. Agarwal, K. Perera, and D. O'Regan, “Multiple positive solutions of singular and nonsingular discrete problems via variational methods,” Nonlinear Analysis: Theory, Methods & Applications, vol. 58, no. 1-2, pp. 69–73, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. C. D. Ahlbrandt, “Dominant and recessive solutions of symmetric three term recurrences,” Journal of Differential Equations, vol. 107, no. 2, pp. 238–258, 1994. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. S. Z. Chen, “Disconjugacy, disfocality, and oscillation of second order difference equations,” Journal of Differential Equations, vol. 107, no. 2, pp. 383–394, 1994. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. S. Z. Chen and L. H. Erbe, “Oscillation and nonoscillation for systems of selfadjoint second-order difference equations,” SIAM Journal on Mathematical Analysis, vol. 20, no. 4, pp. 939–949, 1989. View at Publisher · View at Google Scholar · View at MathSciNet
  5. J. W. Hooker, M. K. Kwong, and W. T. Patula, “Oscillatory second order linear difference equations and Riccati equations,” SIAM Journal on Mathematical Analysis, vol. 18, no. 1, pp. 54–63, 1987. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. Z. M. Guo and J. S. 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 Publisher · View at Google Scholar · View at MathSciNet
  7. Z. M. Guo and J. S. 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
  8. H. H. Bin, J. S. Yu, and Z. M. Guo, “Nontrivial periodic solutions for asymptotically linear resonant difference problem,” Journal of Mathematical Analysis and Applications, vol. 322, no. 1, pp. 477–488, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. J. S. Yu, Z. M. Guo, and X. F. 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
  10. J. S. Yu and Z. M. 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
  11. E. A. B. Silva, “Subharmonic solutions for subquadratic Hamiltonian systems,” Journal of Differential Equations, vol. 115, no. 1, pp. 120–145, 1995. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. J. Mawhin and M. Willem, Critical Point Theory and Hamiltonian Systems, vol. 74 of Applied Mathematical Sciences, Springer, New York, NY, USA, 1989. View at MathSciNet
  13. P. H. Rabinowitz, Minimax Methods in Critical Point Theory with Applications to Differential Equations, vol. 65 of CBMS Regional Conference Series in Mathematics, American Mathematical Society, Providence, RI, USA, 1986. View at MathSciNet
  14. P. Bartolo, V. Benci, and D. Fortunato, “Abstract critical point theorems and applications to some nonlinear problems with strong resonance at infinity,” Nonlinear Analysis: Theory, Methods & Applications, vol. 7, no. 9, pp. 981–1012, 1983. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet