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Lyapunov-type inequalities for the first-order nonlinear Hamiltonian systems. (English) Zbl 1236.34040
Summary: We establish several new Lyapunov-type inequalities for the first-order nonlinear Hamiltonian system which generalize or improve all related existing ones.
34C10Qualitative theory of oscillations of ODE: zeros, disconjugacy and comparison theory
34A40Differential inequalities (ODE)
37J99Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems
[1]Liapunov, A. M.: Problème général de la stabilité du mouvement, Ann. fac. Sci. univ. Toulouse 2, 203-407 (1907)
[2]Wintner, A.: On the non-existence of conjugate points, Amer. J. Math. 73, 368-380 (1951) · Zbl 0043.08703 · doi:10.2307/2372182
[3]Cheng, S. S.: A discrete analogue of the inequality of Lyapunov, Hokkaido math. J. 12, 105-112 (1983) · Zbl 0535.39002
[4]Eliason, S. B.: A Lyapunov inequality for a certain nonlinear differential equation, J. lond. Math. soc. 2, 461-466 (1970)
[5]Hartman, P.; Wintner, A.: On an oscillation criterion of Lyapunov, Amer. J. Math. 73, 885-890 (1951) · Zbl 0043.08704 · doi:10.2307/2372122
[6]Hochstadt, H.: A new proof of a stability estimate of Lyapunov, Proc. amer. Math. soc. 14, 525-526 (1963) · Zbl 0113.07402 · doi:10.2307/2033834
[7]Kwong, M. K.: On Lyapunov’s inequality for disfocality, J. math. Anal. appl. 83, 486-494 (1981) · Zbl 0504.34020 · doi:10.1016/0022-247X(81)90137-2
[8]Nehari, Z.: Some eigenvalue estimates, J. anal. Math. 7, 79-88 (1959) · Zbl 0091.08201 · doi:10.1007/BF02787681
[9]Nehari, Z.: On an inequality of Lyapunov, (1962) · Zbl 0113.07303
[10]Reid, T. W.: A matrix equation related to a non-oscillation criterion and Lyapunov stability, Quart. appl. Math. soc. 23, 83-87 (1965) · Zbl 0132.00701
[11]Reid, T. W.: A matrix Lyapunov inequality, J. math. Anal. appl. 32, 424-434 (1970) · Zbl 0208.11303 · doi:10.1016/0022-247X(70)90308-2
[12]Singh, B.: Forced oscillations in general ordinary differential equations, Tamkang J. Math. 6, 5-11 (1975) · Zbl 0339.34039
[13]Cheng, S. S.: Lyapunov inequalities for differential and difference equations, Fasc. math. 23, 25-41 (1991) · Zbl 0753.34017
[14]Fink, A. M.; Mary, D. F. St.: On an inequality of Nehari, Proc. amer. Math. soc. 21, 640-642 (1969) · Zbl 0179.13502 · doi:10.2307/2036437
[15]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
[16]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
[17]Yang, X.: On inequalities of Lyapunov type, Appl. math. Comput. 134, 293-300 (2003) · Zbl 1030.34018 · doi:10.1016/S0096-3003(01)00283-1
[18]Lee, C.; Yeh, C.; Hong, C.; Agarwal, R. P.: Lyapunov and Wirtinger inequalities, Appl. math. Lett. 17, 847-853 (2004) · Zbl 1062.34005 · doi:10.1016/j.aml.2004.06.016
[19]Tiryaki, A.; Ünal, M.; Cakmak, D.: Lyapunov-type inequalities for nonlinear systems, J. math. Anal. appl. 332, 497-511 (2007) · Zbl 1123.34037 · doi:10.1016/j.jmaa.2006.10.010
[20]Eliason, S. B.: Lyapunov type inequalities for certain second order functional differential equations, SIAM J. Appl. math. 27, No. 1, 180-199 (1974) · Zbl 0292.34077 · doi:10.1137/0127015
[21]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
[22]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
[23]Pachpatte, B. G.: On Lyapunov-type inequalities for certain higher order differential equations, J. math. Anal. appl. 195, 527-536 (1995) · Zbl 0844.34014 · doi:10.1006/jmaa.1995.1372
[24]Pachpatte, B. G.: Inequalities related to the zeros of solutions of certain second order differential equations, Facta univ. Ser. math. Inform. 16, 35-44 (2001) · Zbl 1049.34039
[25]Pinasco, J. P.: Lower bounds for eigenvalues of the one-dimensional p-Laplacian, Abstr. appl. Anal. 2004, 147-153 (2004) · Zbl 1074.34080 · doi:10.1155/S108533750431002X
[26]X.H. Tang, M. Zhang, Lyapunov inequalities and stability for linear Hamiltonian systems, J. Differential Equations, in press (doi:10.1016/j.jde.2011.08.002).