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Journal of Applied Mathematics
Volume 2014 (2014), Article ID 343129, 6 pages
http://dx.doi.org/10.1155/2014/343129
Research Article

Boundary Value Problems for Fourth Order Nonlinear -Laplacian Difference Equations

1School of Mathematics and Information Science, Guangzhou University, Guangzhou, Guangdong 510006, China
2Key Laboratory of Mathematics and Interdisciplinary Sciences of Guangdong Higher Education Institutes, Guangzhou University, Guangzhou, Guangdong 510006, China

Received 6 October 2013; Accepted 26 December 2013; Published 30 January 2014

Academic Editor: Shih-sen Chang

Copyright © 2014 Qinqin Zhang. 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. J. Henderson and H. B. Thompson, “Existence of multiple solutions for second-order discrete boundary value problems,” Computers & Mathematics with Applications, vol. 43, no. 10-11, pp. 1239–1248, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. Y. Li and J. Shu, “Solvability of boundary value problems with Riemann-Stieltjes Δ-integral conditions for second-order dynamic equations on time scales at resonance,” Advances in Difference Equations, vol. 42, pp. 8–18, 2011. View at Google Scholar · View at MathSciNet
  3. R. Ma and C. Gao, “Bifurcation of positive solutions of a nonlinear discrete fourth-order boundary value problem,” Zeitschrift für Angewandte Mathematik und Physik, vol. 64, no. 3, pp. 493–506, 2013. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. C. Yuan, “Positive solutions of a singular positone and semipositone boundary value problems for fourth-order difference equations,” Discrete Dynamics in Nature and Society, vol. 2010, Article ID 312864, 16 pages, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. L. Gao, “Existence of multiple solutions for a second-order difference equation with a parameter,” Applied Mathematics and Computation, vol. 216, no. 5, pp. 1592–1598, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. H. Liang and P. Weng, “Existence and multiple solutions for a second-order difference boundary value problem via critical point theory,” Journal of Mathematical Analysis and Applications, vol. 326, no. 1, pp. 511–520, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. X. Deng and H. Shi, “On boundary value problems for second order nonlinear functional difference equations,” Acta Applicandae Mathematicae, vol. 110, no. 3, pp. 1277–1287, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. J. Liu, S. Wang, and J. Zhang, “Multiple solutions for boundary value problems of second-order difference equations with resonance,” Journal of Mathematical Analysis and Applications, vol. 374, no. 1, pp. 187–196, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. Q. R. Zou and P. X. Weng, “Solutions of 2nth-order boundary value problem for difference equation via variational method,” Advances in Difference Equations, vol. 2009, Article ID 730484, 10 pages, 2009. View at Publisher · View at Google Scholar
  10. D. Bai and Y. Xu, “Nontrivial solutions of boundary value problems of second-order difference equations,” Journal of Mathematical Analysis and Applications, vol. 326, no. 1, pp. 297–302, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. R. Zhang, “Positive solutions of BVPs for third-order discrete nonlinear difference systems,” Journal of Applied Mathematics and Computing, vol. 35, no. 1-2, pp. 551–575, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. J. Yu and Z. Guo, “Boundary value problems of discrete generalized Emden-Fowler equation,” Science in China A, vol. 49, no. 10, pp. 1303–1314, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. T. He and Y. Xu, “Positive solutions for nonlinear discrete second-order boundary value problems with parameter dependence,” Journal of Mathematical Analysis and Applications, vol. 379, no. 2, pp. 627–636, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. H. Berger, “Existence of nontrivial solutions of a two point boundary value problem for a 2nth order nonlinear difference equation,” Advances in Dynamical Systems and Applications, vol. 3, no. 1, pp. 131–146, 2008. View at Google Scholar · View at MathSciNet
  15. S. Xie and J. Zhu, “Positive solutions of the system for nth-order singular nonlocal boundary value problems,” Journal of Applied Mathematics and Computing, vol. 37, no. 1-2, pp. 119–132, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  16. S. Huang and Z. Zhou, “On the nonexistence and existence of solutions for a fourth-order discrete boundary value problem,” Advances in Difference Equations, vol. 2009, Article ID 389624, 18 pages, 2009. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. R. P. Agarwal, Difference Equations and Inequalities: Theory, Methods, and Applications, vol. 228, Marcel Dekker, New York, NY, USA, 2000. View at MathSciNet
  18. H. Shi, Z. Liu, and Z. Wang, “Dirichlet boundary value problems for second order p-Laplacian difference equations,” Rendiconti dell'Istituto di Matematica dell'Università di Trieste, vol. 42, pp. 19–29, 2010. View at Google Scholar · View at MathSciNet
  19. X. Liu, Y. Zhang, B. Zheng, and H. Shi, “Periodic and subharmonic solutions for second order p-Laplacian difference equations,” Indian Academy of Sciences, vol. 121, no. 4, pp. 457–468, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  20. J. Mawhin, “Periodic solutions of second order nonlinear difference systems with p-Laplacian: a variational approach,” Nonlinear Analysis: Theory, Methods & Applications, vol. 75, no. 12, pp. 4672–4687, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  21. Z. Zhou, J. Yu, and Z. Guo, “Periodic solutions of higher-dimensional discrete systems,” Proceedings of the Royal Society of Edinburgh A, vol. 134, no. 5, pp. 1013–1022, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  22. P. H. Rabinowitz, Minimax Methods in Critical Point Theory with Applications to Differential Equations, vol. 65, American Mathematical Society, Providence, RI, USA, 1986. View at MathSciNet