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International Journal of Differential Equations
Volume 2013 (2013), Article ID 740980, 11 pages
Characterization for Rectifiable and Nonrectifiable Attractivity of Nonautonomous Systems of Linear Differential Equations
1Ehime University, Matsuyama 790-8577, Japan
2Department of Mathematics, University of Zagreb, FER, 10000 Zagreb, Croatia
Received 2 April 2013; Accepted 21 May 2013
Academic Editor: Norio Yoshida
Copyright © 2013 Yūki Naito 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.
- K. Falconer, Fractal Geometry, Mathematical Foundations and Applications, John Wiley & Sons, 1999.
- P. Mattila, Geometry of Sets and Measures in Euclidean Spaces, vol. 44 of Fractals and Rectifiability, Cambridge University Press, Cambridge, UK, 1995.
- C. Tricot, Curves and Fractal Dimension, Springer, New York, NY, USA, 1995.
- S. Miličić and M. Pašić, “Nonautonomous differential equations in Banach space and nonrectifiable attractivity in two-dimensional linear differential systems,” Abstract and Applied Analysis, vol. 2013, Article ID 935089, 10 pages, 2013.
- W. A. Coppel, Stability and Asymptotic Behavior of Differential Equations, D. C. Heath and Co., Boston, Mass, USA, 1965.
- L. Cesari, Asymptotic Behavior and Stability Problems in Ordinary Differential Equations, Springer, New York, NY, USA, 3rd edition, 1971.
- I. T. Kiguradze, Some Singular Boundary Value Problems for Ordinary Differential Equations, Izdatel'stvo Tbilisskogo Universiteta, Tbilisi, Ga, USA, 1975.
- P. Hartman, Ordinary Differential Equations, Birkhäuser, Boston, Mass, USA, 2nd edition, 1982.
- M. Pinto, “Asymptotic integration of second-order linear differential equations,” Journal of Mathematical Analysis and Applications, vol. 111, no. 2, pp. 388–406, 1985.
- J. Rovder, “Asymptotic and oscillatory behaviour of solutions of a linear differential equation,” Journal of Computational and Applied Mathematics, vol. 41, no. 1-2, pp. 41–47, 1992.
- 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.
- I. Rachunkova and I. Rachunek, “Asymptotic formula for oscillatory solutions of some singular nonlinear differential equation,” Abstract and Applied Analysis, vol. 2011, Article ID 981401, 9 pages, 2011.
- J. Jaros and T. Kusano, “Existence and precise asymptotic behavior of strongly monotone solutions of systems of nonlinear differential equations,” Difference Equations and Their Applications, vol. 5, pp. 185–204, 2013.
- M. Fečkan, Bifurcation and Chaos in Discontinuous and Continuous Systems, Nonlinear Physical Science, Springer, 2011.
- O. G. Mustafa and Y. V. Rogovchenko, “Asymptotic integration of a class of nonlinear differential equations,” Applied Mathematics Letters, vol. 19, no. 9, pp. 849–853, 2006.
- M. Rasmussen, Attractivity and Bifurcation for Nonautonomous Dynamical Systems, vol. 1907 of Lecture Notes in Mathematics, Springer, Berlin, Germany, 2007.
- L. Hatvani, “On the asymptotic stability for a two-dimensional linear nonautonomous differential system,” Nonlinear Analysis: Theory, Methods & Applications, vol. 25, no. 9-10, pp. 991–1002, 1995.
- J. Sugie and M. Onitsuka, “Integral conditions on the uniform asymptotic stability for two-dimensional linear systems with time-varying coefficients,” Proceedings of the American Mathematical Society, vol. 138, no. 7, pp. 2493–2503, 2010.
- 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, 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.
- 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.
- 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. Pašić, “Rectifiable and unrectifiable oscillations for a class of second-order linear differential equations of Euler type,” Journal of Mathematical Analysis and Applications, vol. 335, no. 1, pp. 724–738, 2007.
- M. Pašić and J. S. W. Wong, “Rectifiable oscillations in second-order half-linear differential equations,” Annali di Matematica Pura ed Applicata. Series IV, vol. 188, no. 3, pp. 517–541, 2009.
- M. Pašić and S. Tanaka, “Rectifiable oscillations of self-adjoint and damped linear differential equations of second-order,” Journal of Mathematical Analysis and Applications, vol. 381, no. 1, pp. 27–42, 2011.
- J. S. W. Wong, “On rectifiable oscillation of Euler type second order linear differential equations,” Electronic Journal of Qualitative Theory of Differential Equations, vol. 20, pp. 1–12, 2007.
- J. S. W. Wong, “On rectifiable oscillation of Emden-Fowler equations,” Memoirs on Differential Equations and Mathematical Physics, vol. 42, pp. 127–144, 2007.
- L. C. Evans and R. F. Gariepy, Measure Theory and Fine Properties of Functions, CRC Press, New York, NY, USA, 1999.