- About this Journal ·
- Abstracting and Indexing ·
- 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 2013 (2013), Article ID 740568, 11 pages
Oscillation Criteria for Fourth-Order Nonlinear Dynamic Equations on Time Scales
1College of Mathematics and Information Science, Guangxi University, Nanning, Guangxi 530004, China
2Department of Mathematics, Guangxi College of Finance and Economics, Nanning, Guangxi 530003, China
Received 6 May 2013; Revised 20 June 2013; Accepted 21 June 2013
Academic Editor: Delfim F. M. Torres
Copyright © 2013 Xin Wu et al. 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.
- 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.
- V. Kac and P. Cheung, Quantum Calculus, Universitext, 2002.
- M. Bohner and A. Peterson, Dynamic Equations on Time Scales: An Introduction with Applications, Birkhäuser, Boston, Mass, USA, 2001.
- M. Bohner and A. Peterson, Advances in Dynamic Equations on Time Scales, Birkhäuser, Boston, Mass, USA, 2003.
- T. Sun, H. Xi, and X. Peng, “Asymptotic behavior of solutions of higher-order dynamic equations on time scales,” Advances in Difference Equations, vol. 2011, Article ID 237219, 14 pages, 2011.
- T. Sun, H. Xi, X. Peng, and W. Yu, “Nonoscillatory solutions for higher-order neutral dynamic equations on time scales,” Abstract and Applied Analysis, vol. 2010, Article ID 428963, 16 pages, 2010.
- T. Sun, H. Xi, and W. Yu, “Asymptotic behaviors of higher order nonlinear dynamic equations on time scales,” Journal of Applied Mathematics and Computing, vol. 37, no. 1-2, pp. 177–192, 2011.
- T. Sun, W. Yu, and H. Xi, “Oscillatory behavior and comparison for higher order nonlinear dynamic equations on time scales,” Journal of Applied Mathematics & Informatics, vol. 30, no. 1-2, pp. 289–304, 2012.
- T. S. Hassan, “Oscillation of third order nonlinear delay dynamic equations on time scales,” Mathematical and Computer Modelling, vol. 49, no. 7-8, pp. 1573–1586, 2009.
- L. Erbe, A. Peterson, and S. H. Saker, “Asymptotic behavior of solutions of a third-order nonlinear dynamic equation on time scales,” Journal of Computational and Applied Mathematics, vol. 181, no. 1, pp. 92–102, 2005.
- L. Erbe, A. Peterson, and S. H. Saker, “Oscillation and asymptotic behavior of a third-order nonlinear dynamic equation,” The Canadian Applied Mathematics Quarterly, vol. 14, no. 2, pp. 129–147, 2006.
- L. Erbe, A. Peterson, and S. H. Saker, “Hille and Nehari type criteria for third-order dynamic equations,” Journal of Mathematical Analysis and Applications, vol. 329, no. 1, pp. 112–131, 2007.
- T. Li, Z. Han, S. Sun, and Y. Zhao, “Oscillation results for third order nonlinear delay dynamic equations on time scales,” Bulletin of the Malaysian Mathematical Sciences Society, vol. 34, no. 3, pp. 639–648, 2011.
- Y. Wang and Z. Xu, “Asymptotic properties of solutions of certain third-order dynamic equations,” Journal of Computational and Applied Mathematics, vol. 236, no. 9, pp. 2354–2366, 2012.
- L. Erbe, T. S. Hassan, and A. Peterson, “Oscillation of third order nonlinear functional dynamic equations on time scales,” Differential Equations and Dynamical Systems, vol. 18, no. 1-2, pp. 199–227, 2010.
- Y. Qi and J. Yu, “Oscillation criteria for fourth-order nonlinear delay dynamic equations,” Electronic Journal of Differential Equations, vol. 2013, no. 79, pp. 1–17, 2013.
- S. R. Grace, M. Bohner, and S. Sun, “Oscillation of fourth-order dynamic equations,” Hacettepe Journal of Mathematics and Statistics, vol. 39, no. 4, pp. 545–553, 2010.
- S. R. Grace, S. Sun, and Y. Wang, “On the oscillation of fourth order strongly superlinear and strongly sublinear dynamic equations,” Journal of Applied Mathematics and Computing, 2013.
- R. P. Agarwal, M. Bohner, T. Li, and C. Zhang, “Oscillation theorems for fourth-order half-linear delay dynamic equations with damping,” Mediterranean Journal of Mathematics, 2013.
- C. Zhang, T. Li, R. P. Agarwal, and M. Bohner, “Oscillation results for fourth-order nonlinear dynamic equations,” Applied Mathematics Letters, vol. 25, no. 12, pp. 2058–2065, 2012.