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