- 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 935089, 10 pages
Nonautonomous Differential Equations in Banach Space and Nonrectifiable Attractivity in Two-Dimensional Linear Differential Systems
University of Zagreb, Faculty of Electrical Engineering and Computing, Department of Mathematics, 10000 Zagreb, Croatia
Received 24 January 2013; Accepted 18 March 2013
Academic Editor: Elena Braverman
Copyright © 2013 Siniša Miličić and Mervan Pašić. 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.
- F. Amato, M. Ariola, M. Carbone, and C. Cosentino, “Finite-time control of linear systems: a survey,” in Current Trends in Nonlinear Systems and Control, Systems & Control: Foundations & Applications, pp. 195–213, Birkhäuser, Boston, Mass, USA, 2006.
- G. Haller, “A variational theory of hyperbolic Lagrangian coherent structures,” Physica D, vol. 240, no. 7, pp. 574–598, 2011.
- T. Peacock and J. Dabiri, “Introduction to focus issue: lagrangian coherent structures,” Chaos, vol. 20, no. 1, Article ID 017501, 2010.
- K. Rateitschak and O. Wolkenhauer, “Thresholds in transient dynamics of signal transduction pathways,” Journal of Theoretical Biology, vol. 264, no. 2, pp. 334–346, 2010.
- I. Rachůnková and L. Rachůnek, “Asymptotic formula for oscillatory solutions of some singular nonlinear differential equation,” Abstract and Applied Analysis, vol. 2011, Article ID 981401, 9 pages, 2011.
- B. B. Singh and I. M. Chandarki, “On the asymptotic behaviours of solutions of third order non-linear autonomous differential equation governing the MHD flow,” Differential Equations & Applications, vol. 3, no. 3, pp. 385–397, 2011.
- P. Hartman, Ordinary Differential Equations, Birkhäauser, Boston, Mass, USA, 2nd edition, 1982.
- W. A. Coppel, Stability and Asymptotic Behavior of Differential Equations, D. C. Heath and Co., Boston, Mass, USA, 1965.
- S. Castillo and M. Pinto, “Asymptotic integration of ordinary different systems,” Journal of Mathematical Analysis and Applications, vol. 218, no. 1, pp. 1–12, 1998.
- S. Bodine, “A dynamical systems result on asymptotic integration of linear differential systems,” Journal of Differential Equations, vol. 187, no. 1, pp. 1–22, 2003.
- R. Medina and M. Pinto, “On the asymptotic behavior of solutions of certain second order nonlinear differential equations,” Journal of Mathematical Analysis and Applications, vol. 135, no. 2, pp. 399–405, 1988.
- H. Matsunaga, “Stability switches in a system of linear differential equations with diagonal delay,” Applied Mathematics and Computation, vol. 212, no. 1, pp. 145–152, 2009.
- S. K. Choi and N. J. Koo, “Asymptotic property for linear integro-differential systems,” Nonlinear Analysis: Theory, Methods & Applications, vol. 70, no. 5, pp. 1862–1872, 2009.
- S. K. Choi, N. J. Koo, and S. Dontha, “Asymptotic property in variation for nonlinear differential systems,” Applied Mathematics Letters, vol. 18, no. 1, pp. 117–126, 2005.
- C. Qian and Y. Sun, “Global attractivity of solutions of nonlinear delay differential equations with a forcing term,” Nonlinear Analysis: Theory, Methods & Applications, vol. 66, no. 3, pp. 689–703, 2007.
- S. Miličić, Geometric and fractal properties of solutions of linear differential systems [Ph.D. thesis], University of Zagreb, Zagreb, Croatia.
- K. Falconer, Fractal Geometry: Mathematical Fondations and Applications, John Wiley & Sons, New York, NY, USA, 1999.
- C. Tricot, Curves and Fractal Dimension, Springer, New York, NY, USA, 1995.
- L. C. Evans and R. F. Gariepy, Measure Theory and Fine Properties of Functions, CRC Press, New York, NY, USA, 1999.
- M. K. Kwong, M. Pašić, and J. S. W. Wong, “Rectifiable oscillations in second-order linear differential equations,” Journal of Differential Equations, vol. 245, no. 8, pp. 2333–2351, 2008.
- M. Onitsuka and J. Sugie, “Uniform global asymptotic stability for half-linear differential systems with time-varying coefficients,” Proceedings of the Royal Society of Edinburgh A, vol. 141, no. 5, pp. 1083–1101, 2011.
- Ju. L. Daleckii and M. G. Kreĭn, Stability of Solutions of Differential Equations in Banach Space, vol. 43 of Translations of Mathematical Monographs, American Mathematical Society, Providence, RI, USA, 1974.
- S. G. Kreĭn, Linear Differential Equations in Banach Space, vol. 29 of Translations of Mathematical Monographs, American Mathematical Society, Providence, RI, USA, 1971.
- A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, vol. 44 of Applied Mathematical Sciences, Springer, New York, NY, USA, 1983.
- A. Favini and E. Obrecht, Differential Equations in Banach Spaces, vol. 1223 of Lectures notes in Mahtematics, Springer, New York, NY, USA, 1985.
- L. H. Hao and K. Schmitt, “Fixed point theorems of Krasnoselskii type in locally convex spaces and applications to integral equations,” Results in Mathematics, vol. 25, no. 3-4, pp. 290–314, 1994.
- C. Avramescu, “Some remarks on a fixed point theorem of Krasnoselskii,” Electronic Journal of Qualitative Theory of Differential Equations, vol. 2003, no. 5, pp. 1–15, 2003.
- L. T. P. Ngoc and N. T. Long, “On a fixed point theorem of Krasnoselskii type and application to integral equations,” Fixed Point Theory and Applications, vol. 2006, Article ID 30847, 24 pages, 2006.
- L. T. P. Ngoc and N. T. Long, “Applying a fixed point theorem of Krasnosel'skii type to the existence of asymptotically stable solutions for a Volterra-Hammerstein integral equation,” Nonlinear Analysis: Theory, Methods & Applications, vol. 74, no. 11, pp. 3769–3774, 2011.
- S. Lang, Real and Functional Analysis, Springer, New York, NY, USA, 3rd edition, 1993.
- S. Roman, Advanced Linear Algebra, Springer, New York, NY, USA, 2008.