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Journal of Function Spaces
Volume 2014, Article ID 815170, 6 pages
http://dx.doi.org/10.1155/2014/815170
Research Article

Existence of Positive Solutions for Second-Order Neumann Difference System

Department of Mathematics, Northwest Normal University, Lanzhou 730070, China

Received 30 October 2013; Accepted 20 December 2013; Published 8 January 2014

Academic Editor: Gen-Qi Xu

Copyright © 2014 Yanqiong Lu and Ruyun Ma. 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. A. Lasota, “A discrete boundary value problem,” Annales Polonici Mathematici, vol. 20, pp. 183–190, 1968. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. R. P. Agarwal, “Difference equations and inequalities,” in Theory, Methods, and Applications, vol. 228 of Monographs and Textbooks in Pure and Applied Mathematics, Marcel Dekker, New York, NY, USA, 2nd edition, 2000. View at Google Scholar
  3. W. G. Kelley and A. C. Peterson, “Difference equations,” in An Introduction With Applications, Harcourt/Academic Press, San Diego, Calif, USA, 2nd edition, 2001. View at Google Scholar
  4. A. Cabada and V. Otero-Espinar, “Fixed sign solutions of second-order difference equations with Neumann boundary conditions,” Computers & Mathematics with Applications, vol. 45, no. 6-9, pp. 1125–1136, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. J.-P. Sun and W.-T. Li, “Existence of positive solutions of boundary value problem for a discrete difference system,” Applied Mathematics and Computation, vol. 156, no. 3, pp. 857–870, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. D. R. Anderson, I. Rachunková, and C. C. Tisdell, “Solvability of discrete Neumann boundary value problems,” Journal of Mathematical Analysis and Applications, vol. 331, no. 1, pp. 736–741, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. J. Henderson, S. K. Ntouyas, and I. K. Purnaras, “Positive solutions for systems of nonlinear discrete boundary value problems,” Journal of Difference Equations and Applications, vol. 15, no. 10, pp. 895–912, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. 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
  9. A. Cañada, P. Magal, and J. A. Montero, “Optimal control of harvesting in a nonlinear elliptic system arising from population dynamics,” Journal of Mathematical Analysis and Applications, vol. 254, no. 2, pp. 571–586, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. S. Li, Z. Xiu, and L. Liang, “Positive solutions for nonlinear singular second order Neumann boundary value problems,” Journal of Mathematical and Computational Science, vol. 2, no. 5, pp. 1353–1362, 2012. View at Google Scholar · View at MathSciNet
  11. R. Chen and Y. Lu, “Existence and multiplicity of positive solutions to nonlinear semipositone Neumann boundary value problem,” Annals of Differential Equations, vol. 28, no. 2, pp. 137–145, 2012. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. L. Y. Zhang, L. Y. Wang, and X. Y. Li, “Multiplicity of positive solutions to second-order singular Neumann boundary value problems for differential systems,” Acta Mathematicae Applicatae Sinica, vol. 31, no. 6, pp. 1035–1045, 2008. View at Google Scholar · View at MathSciNet
  13. G. Sweers, “Strong positivity in C(Ω¯) for elliptic systems,” Mathematische Zeitschrift, vol. 209, no. 2, pp. 251–271, 1992. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. J. López-Gómez and M. Molina-Meyer, “The maximum principle for cooperative weakly coupled elliptic systems and some applications,” Differential and Integral Equations, vol. 7, no. 2, pp. 383–398, 1994. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. K. J. Brown and Y. Zhang, “On a system of reaction-diffusion equations describing a population with two age groups,” Journal of Mathematical Analysis and Applications, vol. 282, no. 2, pp. 444–452, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. R. Ma, “Multiplicity results for a three-point boundary value problem at resonance,” Nonlinear Analysis. Theory, Methods & Applications, vol. 53, no. 6, pp. 777–789, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet