We present some integral inequalities on a time scale and establish sufficient conditions for the uniform stability of an equilibrium state of a nonlinear system on a time scale.
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S. S. Dragomir, The Gronwall Type Lemmas and Applications, Tipografia Univ. Timisoara, Timisoara (1987).
M. Bohner and A. A. Martynyuk, “Elements of stability theory of A. M. Liapunov for dynamic equations on time scales,” Prikl. Mekh., 43, No. 9, 3–27 (2007); English translation: Nonlinear Dyn. Syst. Theory, 7, No. 3, 225–251 (2007).
M. Bohner and A. Peterson, Dynamic Equations on Time Scales: An Introduction with Applications, Birkhäuser, Boston, (2001).
D. B. Pachpatte, “Explicit estimates on integral inequalities with time scale,” J. Inequal. Pure Appl. Math., 7, No. 4 (2006).
M. Bohner, “Some oscillation criteria for first order delay dynamic equations,” Far East J. Appl. Math., 18, No. 3, 289–304 (2005).
A. C. Peterson and Y. N. Raffoul, “Exponential stability of dynamic equations on time scales,” Adv. Difference Equat. , 2005, No. 2, 133–144 (2005).
Yu. A. Martynyuk-Chernienko, “On the theory of stability of motion of a nonlinear system on a time scale,” Ukr. Mat. Zh., 60, No. 6, 776–782 (2008); English translation: Ukr. Math. J., 60, No. 6, 901–909 (2008).
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 62, No. 11, pp. 1490–1499, November, 2010.
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Luk’yanova, T.A., Martynyuk, A.A. Integral inequalities and stability of an equilibrium state on a time scale. Ukr Math J 62, 1729–1740 (2011). https://doi.org/10.1007/s11253-011-0463-6
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DOI: https://doi.org/10.1007/s11253-011-0463-6