OSCILLATORY THEOREMS FOR CERTAIN SECOND ORDER DAMPED DYNAMIC INCLUSIONS WITH DISTRIBUTED DEVIATING ARGUMENTS

TitleOSCILLATORY THEOREMS FOR CERTAIN SECOND ORDER DAMPED DYNAMIC INCLUSIONS WITH DISTRIBUTED DEVIATING ARGUMENTS
Publication TypeJournal Article
Year of Publication2015
AuthorsGRACE, SAID, AKIN, ELVAN, AGARWAL, RAWI
Secondary TitleCommunications in Applied Analysis
Volume19
Issue1
Start Page3
Pagination14
Date Published01/2015
Type of Workscientific: mathematics
ISSN1083–2564
AMS34N05, 39A10.
Abstract
We shall establish some new criteria for the oscillation of second order nonlinear damped dynamic inclusions with distributed deviating arguments on time scales.
URLhttp://www.acadsol.eu/en/articles/19/1/1.pdf
Short TitleSECOND ORDER DAMPED DYNAMIC INCLUSIONS
Refereed DesignationRefereed
Full Text

REFERENCES

[1] E. Akın-Bohner, and S. Sun, Oscillation Criteria for a class of second order strongly superlinear and sublinear dynamic inclusions. Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal., 19, 2012, no. 3, 285–294.
[2] R. P. Agarwal, S. R. Grace and D. O’Regan, Oscillation Theory for Second Order Linear, Half-linear, Superlinear and Sublinear Dynamic Equations. Kluwer, Dordrecht, 2002.
[3] R. P. Agarwal, M. Bohner, S. R. Grace and D. O’Regan, Discrete Oscillation Theory, Hindawi Publishing Corporation, 2005.
[4] R. P. Agarwal, S. R. Grace, D. O’Regan, On nonoscillatory solutions of differential inclusions, Prec. Amer. Math. Soc., 181(2003), 129–140.
[5] R. P. Agarwal, S. R. Grace, D. O’Regan, Oscillation criteria for sublinear and superlinear second order differential inclusions, Mem. Diff. Eqns. Math. Physic. 28(2003), 1–12.
[6] R. P. Agarwal, S. R. Grace, D. O’Regan, Oscillation theorems for second order differential inclusions. Ont. J. Dynamic System. Diff. Eqns., 1(2007), 85–88.
[7] R. P. Agarwal, S. R. Grace, D. O’Regan, Some nonoscillation criteria for inclusions, J. Aust. Math. Soc., 80(2006), 1–12.
[8] R. P. Agarwal, S. R. Grace, D. O’Regan, Oscillation criteria for second order differential inclusions, Adv. Stud. Contem. Math 16(2008), 47–56.
[9] M. Bohner, Some oscillation criteria for first order delay dynamic equations. Far J. Appl. Math. 18(2005), 289–304.
[10] M. Bohner and A. Peterson, Dynamic Equations on Time Scales, An Introduction with Applications, Birkhauser, Boston, 2001.
[11] T. Candan, Oscillation of second order nonlinear neutral dynamic equation on time scales with distributed deviating arguments. Compt. Math. Appl. 62(11)(2011), 471–491.
[12] L. Erbe, A. Peterson and P. Rehak, Comparison theorems for linear dynamic equations on time scales, J. Math. Anal. Appl., 275(2002), 418–438.
[13] L. Erbe, T. Hassan and A. Peterson, Oscillation criteria for nonlinear functional neutral dynamic equations on time scales, J. Diff. Eqn. Appl., 15(2009), 1097–116.
[14] S. R. Grace, R. P. Agarwal and D. O’Regan, A selection of oscillation criteria for second order differential inclusions, Appl. Math Letters. 22(2009), 153–158.
[15] S. R. Grace, R. P. Agarwal, M. Bohner and D. O’Regan, Oscillation of second order strongly superlinear and strongly sublinear dynamic inclusions, Comum. Nonlinear Sci. Numer. Stimul., 14 (2009), 3463–3471.
[16] S. R. Grace, R. P. Agarwal, B. Kaymakalan and W. Sae-jie, Oscillation theorems for second order nonlinear dynamic equations, Appl. Math. Comput., 32(2010), 205–218.
[17] S. R. Grace, E. Akın and M. Dikmen, On the oscillation of second order nonlinear neutral dynamic equations with distributed deviating arguments on time scales, Dynamic Systems and Applications. To appear, 2014.
[18] S. R. Grace, M. Bohner and R. P. Agarwal,On the oscillation of second order half-linear dynamic equations, J. Difference Eqn. Appl., 15(2009), 451–460.
[19] S. Hilger, Analysis on measure chains- a unified approach to continuous and discrete calculus, Results Math., 19(1990), 18–56.
[20] S. H. Saker, Oscillation criteria for second order halflinear dynamic equations on time scales, J. Comput. Appl. Math., 177(2005), 375–387.