- About this Journal ·
- Abstracting and Indexing ·
- Aims and Scope ·
- Annual Issues ·
- Article Processing Charges ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Recently Accepted Articles ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
Abstract and Applied Analysis
Volume 2012 (2012), Article ID 613038, 14 pages
A Generalized Nonuniform Contraction and Lyapunov Function
1Nanjing College of Information Technology, Nanjing 210046, China
2Department of Mathematics, College of Science, Hohai University, Nanjing 210098, China
Received 19 November 2012; Accepted 1 December 2012
Academic Editor: Juntao Sun
Copyright © 2012 Fang-fang Liao 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.
- L. Barreira, J. Chu, and C. Valls, “Robustness of nonuniform dichotomies with different growth rates,” São Paulo Journal of Mathematical Sciences, vol. 5, pp. 1–29, 2011.
- A. M. Lyapunov, The General Problem of the Stability of Motion, Taylor & Francis, 1992.
- W. A. Coppel, Dichotomies in Stability Theory, vol. 629 of Lecture Notes in Mathematics, Springer, Berlin, Germany, 1978.
- W. Hahn, Stability of Motion, Grundlehren der mathematischen Wissenschaften 138, Springer, 1967.
- J. LaSalle and S. Lefschetz, Stability by Liapunov's Direct Method with Applications, vol. 4 of Mathematics in Science and Engineering, Academic Press, 1961.
- Y. A. Mitropolsky, A. M. Samoilenko, and V. L. Kulik, Dichotomies and Stability in Nonautonomous Linear Systems, vol. 14 of Stability and Control: Theory, Methods and Applications, Taylor & Francis, 2003.
- L. Barreira and C. Valls, Stability of Nonautonomous Differential Equations, vol. 1926 of Lecture Notes in Mathematics, Springer, Berlin, Germany, 2008.
- L. Barreira and C. Valls, “Quadratic Lyapunov functions and nonuniform exponential dichotomies,” Journal of Differential Equations, vol. 246, no. 3, pp. 1235–1263, 2009.
- L. Barreira, J. Chu, and C. Valls, “Lyapunov functions for general nonuniform dichotomies,” Preprint.
- L. Barreira and C. Valls, “Lyapunov functions versus exponential contractions,” Mathematische Zeitschrift, vol. 268, no. 1-2, pp. 187–196, 2011.
- J. L. Massera and J. J. Schäffer, “Linear differential equations and functional analysis. I,” Annals of Mathematics, vol. 67, pp. 517–573, 1958.
- O. Perron, “Die Stabilitätsfrage bei Differentialgleichungen,” Mathematische Zeitschrift, vol. 32, no. 1, pp. 703–728, 1930.
- J. Daletskiĭ and M. Kreĭn, Stability of Solutions of Differential Equations in Banach Space, Translations of Mathematical Monographs 43, American Mathematical Society, 1974.
- L. Barreira and C. Valls, “Robustness via Lyapunov functions,” Journal of Differential Equations, vol. 246, no. 7, pp. 2891–2907, 2009.
- S.-N. Chow and H. Leiva, “Existence and roughness of the exponential dichotomy for skew-product semiflow in Banach spaces,” Journal of Differential Equations, vol. 120, no. 2, pp. 429–477, 1995.
- V. A. Pliss and G. R. Sell, “Robustness of exponential dichotomies in infinite-dimensional dynamical systems,” Journal of Dynamics and Differential Equations, vol. 11, no. 3, pp. 471–513, 1999.