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Discrete Dynamics in Nature and Society
Volume 2012 (2012), Article ID 831960, 12 pages
On the Nonhomogeneous Fourth-Order -Laplacian Generalized Sturm-Liouville Nonlocal Boundary Value Problems
1School of Mathematics and Quantitative Economics, Shandong University of Finance and Economics, Shandong, Jinan 250014, China
2School of Mathematical Sciences, Qufu Normal University, Shandong, Qufu 273165, China
Received 3 August 2012; Accepted 12 September 2012
Academic Editor: Yanbin Sang
Copyright © 2012 Jian Liu and Zengqin Zhao. 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.
- H. Feng, W. Ge, and M. Jiang, “Multiple positive solutions for -point boundary-value problems with a one-dimensional -Laplacian,” Nonlinear Analysis. Theory, Methods & Applications, vol. 68, no. 8, pp. 2269–2279, 2008.
- R. P. Agarwal, H. Lü, and D. O'Regan, “Existence theorems for the one-dimensional singular -Laplacian equation with sign changing nonlinearities,” Applied Mathematics and Computation, vol. 143, no. 1, pp. 15–38, 2003.
- C. Zhou and D. Ma, “Existence and iteration of positive solutions for a generalized right-focal boundary value problem with -Laplacian operator,” Journal of Mathematical Analysis and Applications, vol. 324, no. 1, pp. 409–424, 2006.
- Z. Zhao, “Exact solutions of a class of second-order nonlocal boundary value problems and applications,” Applied Mathematics and Computation, vol. 215, no. 5, pp. 1926–1936, 2009.
- Y. Wang and C. Hou, “Existence of multiple positive solutions for one-dimensional -Laplacian,” Journal of Mathematical Analysis and Applications, vol. 315, no. 1, pp. 144–153, 2006.
- Y. Wang and W. Ge, “Positive solutions for multipoint boundary value problems with a one-dimensional -Laplacian,” Nonlinear Analysis. Theory, Methods & Applications, vol. 66, no. 6, pp. 1246–1256, 2007.
- X. Zhang and L. Liu, “A necessary and sufficient condition for positive solutions for fourth-order multi-point boundary value problems with -Laplacian,” Nonlinear Analysis. Theory, Methods & Applications, vol. 68, no. 10, pp. 3127–3137, 2008.
- R. Ma, Nonlocal Problems for the Nonlinear Ordinary Differential Equation, Science Press, Beijing, China, 2004.
- R. W. Leggett and L. R. Williams, “Multiple positive fixed points of nonlinear operators on ordered Banach spaces,” Indiana University Mathematics Journal, vol. 28, no. 4, pp. 673–688, 1979.
- D. J. Guo and V. Lakshmikantham, Nonlinear Problems in Abstract Cones, vol. 5, Academic Press, San Diego, Calif, USA, 1988.