- 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 2011 (2011), Article ID 814962, 16 pages
Conjugacy of Self-Adjoint Difference Equations of Even Order
Department of Mathematics, Mendel University in Brno, Zemědělská 1, 613 00 Brno, Czech Republic
Received 31 January 2011; Revised 5 April 2011; Accepted 18 May 2011
Academic Editor: Elena Braverman
Copyright © 2011 Petr Hasil. 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. Gesztesy and Z. Zhao, “Critical and subcritical Jacobi operators defined as Friedrichs extensions,” Journal of Differential Equations, vol. 103, no. 1, pp. 68–93, 1993.
- O. Došlý and P. Hasil, “Critical higher order Sturm-Liouville difference operators,” to appear in Journal of Difference Equations and Applications.
- O. Došlý, “Existence of conjugate points for selfadjoint linear differential equations,” Proceedings of the Royal Society of Edinburgh. Section A, vol. 113, no. 1-2, pp. 73–85, 1989.
- O. Došlý, “Oscillation criteria and the discreteness of the spectrum of selfadjoint, even order, differential operators,” Proceedings of the Royal Society of Edinburgh. Section A, vol. 119, no. 3-4, pp. 219–232, 1991.
- O. Došlý and J. Komenda, “Conjugacy criteria and principal solutions of self-adjoint differential equations,” Archivum Mathematicum, vol. 31, no. 3, pp. 217–238, 1995.
- M. Bohner, “Linear Hamiltonian difference systems: disconjugacy and Jacobi-type conditions,” Journal of Mathematical Analysis and Applications, vol. 199, no. 3, pp. 804–826, 1996.
- M. Bohner, O. Došlý, and W. Kratz, “A Sturmian theorem for recessive solutions of linear Hamiltonian difference systems,” Applied Mathematics Letters, vol. 12, no. 2, pp. 101–106, 1999.
- O. Došlý, “Transformations of linear Hamiltonian difference systems and some of their applications,” Journal of Mathematical Analysis and Applications, vol. 191, no. 2, pp. 250–265, 1995.
- O. Došlý, “Symplectic difference systems: oscillation theory and hyperbolic Prüfer transformation,” Abstract and Applied Analysis, vol. 2004, no. 4, pp. 285–294, 2004.
- L. H. Erbe and P. X. Yan, “Disconjugacy for linear Hamiltonian difference systems,” Journal of Mathematical Analysis and Applications, vol. 167, no. 2, pp. 355–367, 1992.
- L. H. Erbe and P. X. Yan, “Qualitative properties of Hamiltonian difference systems,” Journal of Mathematical Analysis and Applications, vol. 171, no. 2, pp. 334–345, 1992.
- C. D. Ahlbrandt and A. C. Peterson, Discrete Hamiltonian Systems: Difference Equations, Continued Fractions, and Riccati Equations, Kluwer Academic Publishers, Dordrecht, The Netherlands, 2010.
- W. Kratz, Quadratic Functionals in Variational Analysis and Control Theory, vol. 6 of Mathematical Topics, Akademie, Berlin, Germany, 1995.
- M. Bohner and O. Došlý, “Disconjugacy and transformations for symplectic systems,” The Rocky Mountain Journal of Mathematics, vol. 27, no. 3, pp. 707–743, 1997.
- M. Bohner and S. Stević, “Trench's perturbation theorem for dynamic equations,” Discrete Dynamics in Nature and Society, vol. 2007, Article ID 75672, 11 pages, 2007.
- M. Bohner and S. Stević, “Linear perturbations of a nonoscillatory second-order dynamic equation,” Journal of Difference Equations and Applications, vol. 15, no. 11-12, pp. 1211–1221, 2009.
- O. Došlý, “Oscillation criteria for higher order Sturm-Liouville difference equations,” Journal of Difference Equations and Applications, vol. 4, no. 5, pp. 425–450, 1998.
- P. Hartman, “Difference equations: disconjugacy, principal solutions, Green's functions, complete monotonicity,” Transactions of the American Mathematical Society, vol. 246, pp. 1–30, 1978.
- R. P. Agarwal, Difference Equations and Inequalities, Theory, Methods, and Applications, vol. 155 of Monographs and Textbooks in Pure and Applied Mathematics, Marcel Dekker, New York, NY, USA, 1992.
- P. Hasil, “Criterion of p-criticality for one term 2n-order difference operators,” Archivum Mathematicum, vol. 47, pp. 99–109, 2011.
- W. Kratz, “Banded matrices and difference equations,” Linear Algebra and Its Applications, vol. 337, pp. 1–20, 2001.