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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 107276, 18 pages
http://dx.doi.org/10.1155/2012/107276
Research Article

Existence of Positive Solutions for Multi-Point Boundary Value Problems on Infinite Intervals in Banach Spaces

School of Mathematical Sciences, Qufu Normal University, Shandong, Qufu 273165, China

Received 18 July 2012; Accepted 12 September 2012

Academic Editor: Xinguang Zhang

Copyright © 2012 Zhaocai Hao and Liang 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. S. Z. Chen and Y. Zhang, “Singular boundary value problems on a half-line,” Journal of Mathematical Analysis and Applications, vol. 195, no. 2, pp. 449–468, 1995. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  2. D. O'Regan, Theory of Singular Boundary Value Problems, World Scientific Publishing, River Edge, NJ, USA, 1994. View at Publisher · View at Google Scholar
  3. Y. Liu, “Existence and unboundedness of positive solutions for singular boundary value problems on half-line,” Applied Mathematics and Computation, vol. 144, no. 2-3, pp. 543–556, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  4. H. Lian and W. Ge, “Solvability for second-order three-point boundary value problems on a half-line,” Applied Mathematics Letters, vol. 19, no. 10, pp. 1000–1006, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  5. B. Yan, D. O'Regan, and R. P. Agarwal, “Unbounded solutions for singular boundary value problems on the semi-infinite interval: upper and lower solutions and multiplicity,” Journal of Computational and Applied Mathematics, vol. 197, no. 2, pp. 365–386, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  6. X. Zhang, “Successive iteration and positive solutions for a second-order multi-point boundary value problem on a half-line,” Computers & Mathematics with Applications, vol. 58, no. 3, pp. 528–535, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  7. Y. Liu, “Boundary value problems for second order differential equations on unbounded domains in a Banach space,” Applied Mathematics and Computation, vol. 135, no. 2-3, pp. 569–583, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  8. X. Zhang, “Existence of positive solutions for multi-point boundary value problems on infinite intervals in Banach spaces,” Applied Mathematics and Computation, vol. 206, no. 2, pp. 932–941, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  9. D. Guo, “Multiple positive solutions for nth-order impulsive integro-differential equations in Banach spaces,” Nonlinear Analysis: Theory, Methods & Applications, vol. 60, no. 5, pp. 955–976, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  10. D. Guo, V. Lakshmikantham, and X. Liu, Nonlinear Integral Equations in Abstract Spaces, vol. 373 of Mathematics and Its Applications, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1996.
  11. D. Guo, “Existence of solutions for nth order impulsive integro-differential equations in a banach space,” Nonlinear Analysis, Theory, Methods and Applications, vol. 47, no. 2, pp. 741–752, 2001. View at Publisher · View at Google Scholar · View at Scopus
  12. K. Deimling, Ordinary Differential Equations in Banach Spaces, vol. 596 of Lecture Notes in Mathematics, Springer, Berlin, Germany, 1977.
  13. V. Lakshmikantham and S. Leela, Nonlinear Differential Equations in Abstract Spaces, vol. 2 of International Series in Nonlinear Mathematics: Theory, Methods and Applications, Pergamon Press, Oxford, UK, 1981.