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Lyapunov inequalities and stability for discrete linear Hamiltonian systems. (English) Zbl 1229.39026
Authors’ abstract: We establish several new Lyapunov type inequalities for discrete linear Hamiltonian systems when the end-points are not necessarily usual zeros, but rather, generalized zeros, which generalize and improve almost all related existing ones. Applying these inequalities, an optimal stability criterion is obtained.

39A30Stability theory (difference equations)
39A06Linear equations (difference equations)
39A12Discrete version of topics in analysis
37J25Stability problems (finite-dimensional Hamiltonian etc. systems)
Full Text: DOI
[1] Aubry, S.: Discrete breathers: localization and transfer of energy in discrete Hamiltonian nonlinear systems, Review article physica D: Nonlinear phenomena 216, 1-30 (2006) · Zbl 1159.82312 · doi:10.1016/j.physd.2005.12.020
[2] Bohner, M.: Linear Hamiltonian difference systems: disconjugacy and Jacobi-type conditions, J. math. Anal. appl 199, 804-826 (1996) · Zbl 0855.39018 · doi:10.1006/jmaa.1996.0177
[3] Bohner, M.: Discrete linear Hamiltonian eigenvalue problems, Comput. math. Appl. 36, 179-192 (1998) · Zbl 0933.39033 · doi:10.1016/S0898-1221(98)80019-9
[4] Erbe, L. H.; Yan, P. X.: Disconjugacy for linear Hamiltonian difference systems, J. math. Anal. appl. 167, 355-367 (1992) · Zbl 0762.39003 · doi:10.1016/0022-247X(92)90212-V
[5] Shi, Y. M.: Spectral theory of discrete linear Hamiltonian systems, J. math. Anal. appl 289, 554-570 (2004) · Zbl 1047.39016 · doi:10.1016/j.jmaa.2003.08.039
[6] Shi, Y. M.: Weyl -- titchmarsh theory for a class of discrete linear Hamiltonian systems, Linear algebra appl. 416, 452-519 (2006) · Zbl 1100.39020 · doi:10.1016/j.laa.2005.11.025
[7] Sun, H. Q.; Shi, Y. M.: Strong limit point criteria for a class of singular discrete linear Hamiltonian systems, J. math. Anal. appl. 336, 224-242 (2007) · Zbl 1132.39014 · doi:10.1016/j.jmaa.2007.02.058
[8] Yu, J. S.; Bin, H. H.; Guo, Z. M.: Multiple periodic solutions for discrete Hamiltonian systems, Nonlinear anal 66, 1498-1512 (2007) · Zbl 1115.39017 · doi:10.1016/j.na.2006.01.029
[9] Hartman, P.: Difference equations: disconjugacy, principal solutions, Green’s functions, complete monotonicity, Trans. amer. Math. soc. 246, 1-30 (1978) · Zbl 0409.39001 · doi:10.2307/1997963
[10] Agarwal, R.; Ahlbrandt, C. D.; Bohner, M.; Peterson, A. C.: Discrete linear Hamiltonian systems: a survey, Dynam. syst. Appl. 8, 307-333 (1999) · Zbl 0942.39009
[11] Ahlbrandt, C. D.; Peterson, A. C.: Discrete Hamiltonian systems: difference equations, continued fractions, and Riccati equations, (1996) · Zbl 0860.39001
[12] Bohner, M.; Clark, S.; Ridenhour, J.: Lyapunov inequalities on time scales, J. inequal. Appl. 7, 61-77 (2002) · Zbl 1088.34503 · doi:10.1155/S102558340200005X
[13] Cheng, S. S.: A discrete analogue of the inequality of Lyapunov, Hokkaido math. J. 12, 105-112 (1983) · Zbl 0535.39002
[14] Cheng, S. S.: Lyapunov inequalities for differential and difference equations, Fasc. math. 23, 25-41 (1991) · Zbl 0753.34017
[15] Clark, S.; Hinton, D. B.: Discrete Lyapunov inequalities for linear Hamiltonian systems, Math. inequal. Appl. 1, 201-209 (1998) · Zbl 0909.34033
[16] Clark, S.; Hinton, D. B.: Discrete Lyapunov inequalities, Dynam. syst. Appl. 8, 369-380 (1999) · Zbl 0940.39013
[17] Guseinov, G. Sh.; Zafer, A.: Stability criteria for linear periodic impulsive Hamiltonian systems, J. math. Anal. appl. 335, 1195-1206 (2007) · Zbl 1128.34005 · doi:10.1016/j.jmaa.2007.01.095
[18] Guseinov, G. Sh.; Kaymakcalan, B.: Lyapunov inequalities for discrete linear Hamiltonian systems, Comput. math. Appl. 45, 1399-1416 (2003) · Zbl 1055.39029 · doi:10.1016/S0898-1221(03)00095-6
[19] Jiang, L. Q.; Zhou, Z.: Lyapunov inequality for linear Hamiltonian systems on time scales, J. math. Anal. appl. 310, 579-593 (2005) · Zbl 1076.37053 · doi:10.1016/j.jmaa.2005.02.026
[20] M.G. Krein, Foundations of the theory of \lambda -zones of stability of canonical system of linear differential equations with periodic coefficients. In Memory of A.A. Andronov, Izdat. Acad. Nauk SSSR, Moscow, 1955, pp. 413 -- 498 (Amer. Math. Soc. Transl. Ser. 2, 120 (1983) 1 -- 70).
[21] Wang, X.: Stability criteria for linear periodic Hamiltonian systems, J. math. Anal. appl 367, 329-336 (2010) · Zbl 1195.34079 · doi:10.1016/j.jmaa.2010.01.027
[22] Yakubovich, V. A.; Starzhinsky, V. M.: Linear differential equations with periodic coefficients, parts I and II, (1975) · Zbl 0308.34001
[23] Elaydi, S. N.: An introduction to difference equations, (2004) · Zbl 1067.39002