- About this Journal ·
- Abstracting and Indexing ·
- Advance Access ·
- Aims and Scope ·
- Annual Issues ·
- Article Processing Charges ·
- Articles in Press ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
Abstract and Applied Analysis
Volume 2012 (2012), Article ID 798796, 17 pages
Positive Solutions of a Nonlinear Fourth-Order Dynamic Eigenvalue Problem on Time Scales
1School of Mathematics and Quantitative Economics, Dongbei University of Finance and Economics, Dalian 116025, China
2Department of Mathematics, Northwest Normal University, Lanzhou 730070, China
Received 25 December 2011; Accepted 27 March 2012
Academic Editor: Yonghong Wu
Copyright © 2012 Hua Luo and Chenghua Gao. 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.
- C. J. Chyan and J. Henderson, “Eigenvalue problems for nonlinear differential equations on a measure chain,” Journal of Mathematical Analysis and Applications, vol. 245, no. 2, pp. 547–559, 2000.
- D. R. Anderson, “Eigenvalue intervals for a two-point boundary value problem on a measure chain,” Journal of Computational and Applied Mathematics, vol. 141, no. 1-2, pp. 57–64, 2002.
- L. Erbe, A. Peterson, and R. Mathsen, “Existence, multiplicity, and nonexistence of positive solutions to a differential equation on a measure chain,” Journal of Computational and Applied Mathematics, vol. 113, no. 1-2, pp. 365–380, 2000.
- W. T. Li and X. L. Liu, “Eigenvalue problems for second-order nonlinear dynamic equations on time scales,” Journal of Mathematical Analysis and Applications, vol. 318, no. 2, pp. 578–592, 2006.
- H. Luo and R. Ma, “Nodal solutions to nonlinear eigenvalue problems on time scales,” Nonlinear Analysis: Theory, Methods & Applications, vol. 65, no. 4, pp. 773–784, 2006.
- H. R. Sun, L. T. Tang, and Y. H. Wang, “Eigenvalue problem for p-Laplacian three-point boundary value problems on time scales,” Journal of Mathematical Analysis and Applications, vol. 331, no. 1, pp. 248–262, 2007.
- H. Luo, “Positive solutions to singular multi-point dynamic eigenvalue problems with mixed derivatives,” Nonlinear Analysis: Theory, Methods & Applications, vol. 70, no. 4, pp. 1679–1691, 2009.
- L. Kong and Q. Kong, “Even order nonlinear eigenvalue problems on a measure chain,” Nonlinear Analysis: Theory, Methods & Applications, vol. 52, no. 8, pp. 1891–1909, 2003.
- K. L. Boey and P. J. Y. Wong, “Two-point right focal eigenvalue problems on time scales,” Applied Mathematics and Computation, vol. 167, no. 2, pp. 1281–1303, 2005.
- D. B. Wang and J. P. Sun, “Existence of a solution and a positive solution of a boundary value problem for a nonlinear fourth-order dynamic equation,” Nonlinear Analysis: Theory, Methods & Applications, vol. 69, no. 5-6, pp. 1817–1823, 2008.
- I. Y. Karaca, “Fourth-order four-point boundary value problem on time scales,” Applied Mathematics Letters, vol. 21, no. 10, pp. 1057–1063, 2008.
- Y. Pang and Z. Bai, “Upper and lower solution method for a fourth-order four-point boundary value problem on time scales,” Applied Mathematics and Computation, vol. 215, no. 6, pp. 2243–2247, 2009.
- R. P. Agarwal and M. Bohner, “Basic calculus on time scales and some of its applications,” Results in Mathematics, vol. 35, no. 1-2, pp. 3–22, 1999.
- M. Bohner and A. Peterson, Dynamic Equations on Time Scales: An Introduction with Applications, Birkhäuser, Boston, Mass, USA, 2001.
- M. Bohner and A. Peterson, Eds., Advances in Dynamic Equations on Time Scales, Birkhäuser, Boston, Mass, USA, 2003.
- S. Hilger, “Analysis on measure chains—a unified approach to continuous and discrete calculus,” Results in Mathematics, vol. 18, no. 1-2, pp. 18–56, 1990.
- D. Guo, J. Sun, and Z. Liu, Functional Methods of Nonlinear Differential Equations, Shandong Science and Technoledge Press, Shandong, China, 1995.