Publication Cover
Applicable Analysis
An International Journal
Volume 92, 2013 - Issue 8
98
Views
0
CrossRef citations to date
0
Altmetric
Articles

Stability for planar linear discrete Hamiltonian systems with perturbations

, &
Pages 1704-1716 | Received 09 Jan 2012, Accepted 18 May 2012, Published online: 21 Jun 2012

References

  • Agarwal , R , Ahlbrandt , CD , Bohner , M and Peterson , AC . 1999 . Discrete linear Hamiltonian systems . A survey, Dyn. Syst. Appl. , 8 : 307 – 333 .
  • Ahlbrandt , CD and Peterson , AC . 1996 . Discrete Hamiltonian systems: Difference Equations, Continued Fractions, and Riccati Equations , Boston , , MA : Kluwer Academic .
  • Aubry , S . 2006 . Discrete Breathers: Localization and transfer of energy in discrete Hamiltonian nonlinear systems (Review Article) . Phys. D: Nonlinear Phenom. , 216 : 1 – 30 .
  • Bohner , M . 1996 . Linear Hamiltonian difference systems: disconjugacy and Jacobi-type conditions . J. Math. Anal. Appl. , 199 : 804 – 826 .
  • Bohner , M . 1998 . Discrete linear Hamiltonian eigenvalue problems . Comput. Math. Appl. , 36 : 179 – 192 .
  • Erbe , LH and Yan , PX . 1992 . Disconjugacy for linear Hamiltonian difference systems . J. Math. Anal. Appl. , 167 : 355 – 367 .
  • Hartman , P . 1978 . Difference equations: Disconjugacy, principal solutions, Green's functions, complete monotonicity . Trans. Am. Math. Soc. , 246 : 1 – 30 .
  • Shi , YM . 2004 . Spectral theory of discrete linear Hamiltonian systems . J. Math. Anal. Appl. , 289 : 554 – 570 .
  • Shi , YM . 2006 . Weyl-Titchmarsh theory for a class of discrete linear Hamiltonian systems . Linear Algebra Appl. , 416 : 452 – 519 .
  • Sun , HQ and Shi , YM . 2007 . Strong limit point criteria for a class of singular discrete linear Hamiltonian systems . J. Math. Anal. Appl. , 336 : 224 – 242 .
  • Tang , XH and Zhang , M . 2012 . Lyapunov inequalities and stability for linear Hamiltonian systems . J. Differ. Eqns. , 252 : 358 – 381 .
  • Elaydi , SN . 2004 . An Introduction to Difference Equations , 3 , New York : Springer-Verlag .
  • Guseinov , GSh and Kaymakcalan , B . 2003 . Lyapunov inequalities for discrete linear Hamiltonian systems . Comput. Math. Appl. , 45 : 1399 – 1416 .
  • Zhang , Q and Tang , XH . 2011 . Lyapunov inequalities and stability for discrete linear Hamiltonian system . Appl. Math. Comput. , 218 : 574 – 582 .
  • Zhang , Q and Tang , XH . Lyapunov inequalities and stability for discrete linear Hamiltonian systems . J. Differ. Eqns. Appl. , (in press) DOI:10.1080/10236198.2011.572071

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.