Some Remark on Oscillation of Second Order Impulsive Delay Dynamic Equations on Time Scales

[1] AGARWAL, R. P.—BOHNER, M.—PETERSON, A.: Inequality on time scales: A Survay, Math. Inequal. Appl. 4 (2001), 555–557.Search in Google Scholar

[2] AGWA, H. A.—KHODIER, AHMED M. M.—ATTEYA, HEBA M.: Oscillation of second order nonlinear impulsive dynamic equations on time scales, J. Anal. Number Theory 5 (2017), 147–154.10.18576/jant/050209Search in Google Scholar

[3] AGWA, H. A.—KHODIER, AHMED M. M. — ATTEYA, HEBA M.: Oscillation of second order nonlinear impulsive dynamic equations with a damping term on time scales, Acta Math. Univ. Comenian. 1 (2019), 23–38.Search in Google Scholar

[4] BELARBI, A.—BENCHOHRA, M.—OUAHAB, A.: Extremal solutions for impulsive dynamic equations on time scales, Comm. Appl. Nonlinear Anal. 12 (2005), 85–95.Search in Google Scholar

[5] BENCHOHRA, M.—HENDERSON, J.—NTOUYAS, S. K.—OUAHAB, A.: On first order impulsive dynamic equations on time scales, J. Difference Equ. Appl. 10 (2004), 541–548.10.1080/10236190410001667986Search in Google Scholar

[6] BENCHOHRA, M.—NTOUYAS, S. K.—OUAHAB, A.: Extremal solutions of second order impulsive dynamic equations on time scales, J. Math. Anal. Appl. 324 (2006), 425–434.10.1016/j.jmaa.2005.12.028Search in Google Scholar

[7] BOHNER, M.—PETERSON, A.: Dynamic Equations on Time Scales: An Introduction with Applications. Birkhauser, Boston, 2001.10.1007/978-1-4612-0201-1Search in Google Scholar

[8] BOHNER, M.—PETERSON, A.: Advances in Dynamic Equations on Time Scales. Birkhauser, Boston, 2003.10.1007/978-0-8176-8230-9Search in Google Scholar

[9] BOHNER, M.—TISDELL, C.: Oscillation and nonoscillation of forced second order dynamic equations, Pacific J. Math. 230 (2007), 59–71.10.2140/pjm.2007.230.59Search in Google Scholar

[10] KABADA, A.—VIVERO, D. R.: Criterions for absolute continuity on time scales, J. Difference Equ. Appl. 11 (2005), 1013–1028.10.1080/10236190500272830Search in Google Scholar

[11] CHANG, Y. K.—LI, W. T.: Existence results for impulsive dynamic equations on time scales with nonlocal initial conditions, Math. Comput. Modelling 43 (2006), 337–384.Search in Google Scholar

[12] HE, Z. — GE, W.: Oscillation of impulsive delay differential equations, Indian J. Pure Appl. Math. 31 (2000), 1089–1101.Search in Google Scholar

[13] HE, Z. — GE, W.: Oscillation in second order linear delay differential equations with nonlinear impulses, Math. Slovaca. 52 (2002), 331–341.Search in Google Scholar

[14] HARDY, G. H.—LITTLEWOOD, J. E.—POLYA, G.: Inequalities. Second ed., Cambridge University Press, Cambridge, 1952.Search in Google Scholar

[15] HILGER, S.: Analysis on measure chains — a unified approach to continuous and discrete calculus, Results Math. 18 (1990), 1–2, 18–56.Search in Google Scholar

[16] HUANG, M.—FENG, W.: Oscillation of second order nonlinear impulsive dynamic equations on time scales, Electron. J. Differential Equations 72 (2007), 1–13.Search in Google Scholar

[17] HUANG, M.—FENG, W.: Oscillation criteria for impulsive dynamic equations on time scales, Electron. J. Differential Equations 169 (2007), 1–9.Search in Google Scholar

[18] HUANG, M.: Oscillation criteria for second order nonlinear dynamic equations with impulses, Comput. Math. Appl. 59 (2010), 31–41.10.1016/j.camwa.2009.03.039Search in Google Scholar

[19] HUANG, M.—WEN, K.: Oscillation for forced second-order impulsive nonlinear dynamic equations on time scales, Discrete Dyn. Nat. Soc. 2019, Art. ID 7524743, 1–7.Search in Google Scholar

[20] JIAO, J.—CHEN, L.—LI, M.: Asymptotic behaviour of solutions of second order nonlinear impulsive differential equations, J. Math. Anal. Appl. 337 (2008), 458–463.10.1016/j.jmaa.2007.04.021Search in Google Scholar

[21] KAUFMANN, E. R.—KOSMATOV, N.—RAFFOUL, Y. N.: Impulsive dynamic equations on a time scale, Electron. J. Differ. Equ. 69 (2008), 1–9.Search in Google Scholar

[22] KOSLOV, V. V.—TRESHCHEEV, D. V.: Billiards- a genetic introduction to the dynamics of systems with impacts. Amer. Math. Soc. 1991.Search in Google Scholar

[23] LI, Q.—GUO, F.: Oscillation of solutions to impulsive dynamic equations on time scales, Electron. J. Differential Equations 122 (2009), 1–7.Search in Google Scholar

[24] LI, Q.—ZHOU, L.: Oscillation criteria for second order impulsive dynamic equations on time scales, Appl. Math. E-Notes 11 (2011), 33–40.Search in Google Scholar

[25] PENG, M.: Oscillation caused by impulses, J. Math. Anal. Appl. 255 (2001), 163–176.10.1006/jmaa.2000.7218Search in Google Scholar

[26] PENG, M.: Oscillation criteria for second order impulsive delay difference equations, Appl. Math. Comput. 146 (2003), 227–235.Search in Google Scholar

[27] SUN, S.—HAN, Z.—ZHANG, C.: Oscillation of second order delay dynamic equations on time scales, J. Appl. Math. Comput. 30 (2009), 459–468.10.1007/s12190-008-0185-6Search in Google Scholar

[28] ZHANG, Q. — GAO, L.—WANG, L.: Oscillation of second order nonlinear delay dynamic equations on time scales, Comput. Math. Appl. 61 (2011), 2342–2348.10.1016/j.camwa.2010.10.005Search in Google Scholar