___

• Agarwal, R.P., Bohner, M., Peterson, A.C.: Inequalities on time scales: A survey. Math. Inequ. and Appl. 4, 535—557 (2001).
• Agarwal, R.P., Bohner, M., Rehak, P.: H alf—linear dynamic equations: A survey. Nonlinear Analysis and Applications , 1—58 (2003).
• Ahlbrandt, C.D., Peterson, A.C.: Discrete Hamiltonian system: Dişerence equations, continued fractions and Riccati equations. Kluwer Academic, Boston 1996.
• Bohner, M., Peterson, A.C.: Dynamic equations on time scales. Birkhauser, Boston 2001.
• Bohner, M., Peterson, A.C.: Advances in dynamic equations on time scales. Birkhauser, Boston 2002.
• Cheng, S.S.: A discrete analogue of the inequality of Lyapunov. Hokkaido Math. J. 12 , —112 (1983).
• Cheng, S.S.: Lyapunov inequalities for dişerential and dişerence equations. Fasc. Math. 23, (1991).
• Dahiya, R.S., Singh, B.: A Liapunou inequality and nonoscillation theorem for a second order nonlinear dişerentialidiŞference equations. J. Math. Phys. Sci. 7, 163—170 (1973).
• Dosljr, O., Rehak, P.: Half-linear differential equations. Mathematics Studies 202, North- Holland 2005. Bolyai 30, 158—180 (1979).
• Eliason, S.B.: A Lyapunov inequality for a certain nonlinear dişerential equation. J. London Math. Soc. 2, 461466 (1970).
• Eliason, S.B.: Lyapunov type inequalities for certain second order functional dişerential equations. SIAM J. Appl. Math. 27, no. 1, 180—199 (1974).
• Hartman, P.: Ordinary dişerential equations. 2nd. ed., Birkhauser, Boston 1982.
• Hilger, S.: Ein MaBkettenkalkiil mit Anwendung auf Zentrumsmannigfaltigkeiten. PhD the— Hochstadt, H.: A new proof of a stability estimate of Lyapunov. Proc. Amer. Math. Soc. , 525 — 526 (1963).
• Jiang, L., Zhou, Z.: Lyapunou inequality for linear Hamiltonian systems on time scales. J. Kwong, M.K.: On Lyapunou’s inequality for disfocality. J. Math. Anal. Appl. 83, 4864194
• Lee, C., Yeh, C., Hong, C., Agarwal, R.P.: Lyapunou and Wirtinger inequalities. Appl. Math. Letters 17, 847—853 (2004).
• Lakshmikantham, V., Kaymakçalan, B., Sivasundaram, S.: Dynamic systems on measure Liapunov, A.M.: Probleme general de la stabilité du mouvement. vol. 17, Princeton Univ. MaWhin, J., Willem, M.: Critical points theory and Hamiltonian systems. Springer—Verlag, Pachpatte, B.G.: On Lyapunou — type inequalities for certain higher order dişerential equations. J. Math. Anal. Appl. 195, 527—536 (1995).
• Pachpatte, B.G.: Inequalities related to the zeros of solutions of certain second order diğer- ential equations. Facta Universitatis, Ser. Math. Inform. 16, 35414 (2001).
• Pinasco, J.P.: Lower bounds for eigenvalues of the one-dimensional p-Laplacian. Abstract and Applied Analysis 2004, 147—153 (2004).
• Reid, T.W.: A matrix equation related to a non-oscillation criterion and Lyapunou stability. Quart. Appl. Math. Soc. 23, 83—87 (1965).
• Reid, T.W.: A matrix Lyapunou inequality. J. Math. Anal. Appl. 32, 4244134 (1970).
• Singh, B.: Forced oscillations in general ordinary dişerential equations. Tamkang J. Math. , 5—11 (1975).
• Tiryaki, A., Ünal, M., Çakmak, D.: Lyapunov-type inequalities for nonlinear systems. J. Math. Anal. Appl. 332, 497—511 (2007).
• Ünal, M., Çakmak, D., Tiryaki, A.: A discrete analogue of Lyapuno'u-type inequalities for nonlinear systems. Comput. Math. Appl. 55, 2631-2642 (2008).
• Mehmet ÜNAL Received 08.03.2007
• Department of Mathematics and Computer Science, Bahçeşehir University, Beşiktaş, İstanbul—TURKEY e—mail: munal©bahcesehir.edu.tr Devrim ÇAKMAK Department of Mathematics Education, Faculty of Education, Gazi University, 06500 Teknikokullar, Ankara—TURKEY e—mail: dcakmak©gazi.edu.tr