Abstract
We obtain some oscillation criteria for all solutions to a second-order mixed neutral differential equation with distributed deviating arguments. The results presented improve those reported in the literature.
This research is supported by the National Key Basic Research Program of P. R. China (2013CB035604) and the NNSF of P. R. China (Grant Nos. 61034007, 51277116, 51107069)
Acknowledgement
The authors would like to thank Professor Michal Fečkan and the anonymous referees for their thoughtful review of this manuscript and their insightful comments used to improve the quality of this paper.
References
[1] Baculíková, B.: Oscillation criteria for second order nonlinear differential equations, Arch. Math. (Brno) 42 (2006), 141–149.Suche in Google Scholar
[2] Baculíková, B.—Džurina, J.—Li, T.: Oscillation results for even-order quasilinear neutral functional differential equations, Electron. J. Differential Equations 2011 (2011), 1–9.10.14232/ejqtde.2011.1.74Suche in Google Scholar
[3] Baculíková, B.—Li, T.—Džurina, J.: Oscillation theorems for second-order superlinear neutral differential equations, Math. Slovaca 63 (2013), 123–134.10.2478/s12175-012-0087-9Suche in Google Scholar
[4] Candan, T.: Oscillation of solutions for odd-order neutral functional differential equations, Electron. J. Differential Equations 2010 (2010), 1–10.10.1155/2010/184180Suche in Google Scholar
[5] Candan, T.: Oscillation behavior of solutions for even order neutral functional differential equations, Appl. Math. Mech. (English Ed.) 27 (2006), 1311–1320.10.1007/s10483-006-1003-1Suche in Google Scholar
[6] Candan, T.—Dahiya, R. S.: Oscillation of mixed neutral functional differential equations with distributed deviating arguments, Differ. Equ. Dyn. Syst. 16 (2008), 207–223.10.1007/s12591-008-0013-3Suche in Google Scholar
[7] Candan, T.—Dahiya, R. S.: On the oscillation of certain mixed neutral equations, Appl. Math. Lett. 21 (2008), 222–226.10.1016/j.aml.2007.02.021Suche in Google Scholar
[8] Džurina, J.—Busa, J.—Airyan, E. A.: Oscillation criteria for second-order differential equations of neutral type with mixed arguments, Differ. Equ. 38 (2002), 137–140.10.1023/A:1014872030186Suche in Google Scholar
[9] Džurina, J.—Hudáková, D.: Oscillation of second order neutral delay differential equations, Math. Bohem. 134 (2009), 31–38.10.21136/MB.2009.140637Suche in Google Scholar
[10] Grace, S. R.: On the oscillations of mixed neutral equations, J. Math. Anal. Appl. 194 (1995), 377–388.10.1006/jmaa.1995.1306Suche in Google Scholar
[11] Hasanbulli, M.—Rogovchenko, Yu. V.: Oscillation criteria for second order nonlinear neutral differential equations, Appl. Math. Comput. 215 (2010), 4392–4399.10.1016/j.amc.2010.01.001Suche in Google Scholar
[12] Hasanbulli, M.—Rogovchenko, Yu. V.: Asymptotic behavior of nonoscillatory solutions to n-th order nonlinear neutral differential equations, Nonlinear Anal. 69 (2008), 1208–1218.10.1016/j.na.2007.06.025Suche in Google Scholar
[13] Li, T.: Comparison theorems for second-order neutral differential equations of mixed type, Electron. J. Differential Equations 2010 (2010), 1–7.10.1155/2010/215856Suche in Google Scholar
[14] Li, T.—Agarwal, R. P.—Bohner, M.: Some oscillation results for second-order neutral differential equations, J. Indian Math. Soc. 79 (2012), 97–106.Suche in Google Scholar
[15] Li, T.—Baculíková, B.—Džurina, J.: Oscillation results for second-order neutral differential equations of mixed type, Tatra Mt. Math. Publ. 48 (2011), 101–116.10.2478/v10127-011-0010-8Suche in Google Scholar
[16] Li, T.—Han, Z.—Zhang, C.—Li, H.: Oscillation criteria for second-order superlinear neutral differential equations, Abstr. Appl. Anal. 2011 (2011), 1–17.10.1155/2011/328914Suche in Google Scholar
[17] Li, T.—Han, Z.—Zhao, P.—Sun, S.: Oscillation of even-order neutral delay differential equations, Adv. Difference Equ. 2010 (2010), 1–9.10.1155/2010/727486Suche in Google Scholar
[18] Li, T.—Rogovchenko, Yu. V.—Zhang, C.: Oscillation of second-order neutral differential equations, Funkcial. Ekvac. 56 (2013), 111–120.10.1619/fesi.56.111Suche in Google Scholar
[19] Li, T.—Şenel, M. T.—Zhang, C.: Oscillation of solutions to second-order half-linear differential equations with neutral terms, Electron. J. Differential Equations 2013 (2013), 1–7.10.1155/2013/802324Suche in Google Scholar
[20] Qi, Y.—Yu, J.: Oscillation of second order nonlinear mixed neutral differential equations with distributed deviating arguments, Bull. Malays. Math. Sci. Soc. (2) 38 (2015), 543–560.10.1007/s40840-014-0035-7Suche in Google Scholar
[21] Thandapani, E.—Piramanantham, V.: Oscillation criteria of second order neutral delay dynamic equations with distributed deviating arguments, Electron. J. Qual. Theory Differ. Equ. 2010 (2010), 1–15.10.14232/ejqtde.2010.1.61Suche in Google Scholar
[22] Wang, P. G.: Oscillation criteria for second order neutral equations with distributed deviating arguments, Comput. Math. Appl. 47 (2004), 1935–1946.10.1016/j.camwa.2002.10.016Suche in Google Scholar
[23] Wang, P. G.—Teo, K. L.—Liu, Y. Q.: Oscillation properties for even order neutral equations with distributed deviating arguments, J. Comput. Appl. Math. 182 (2005), 290–303.10.1016/j.cam.2004.12.010Suche in Google Scholar
[24] Xu, Z. T.—Weng, P. X.: Oscillation of second-order neutral equations with distributed deviating arguments, J. Comput. Appl. Math. 202 (2007), 460–477.10.1016/j.cam.2006.03.001Suche in Google Scholar
[25] Yan, J. R.: Oscillation of higher order neutral differential equations, J. Austral. Math. Soc. Ser. A 64 (1998), 73–81.10.1017/S1446788700001300Suche in Google Scholar
[26] Yu, Y. H.—Fu, X. L.: Oscillation of second order neutral equation with continuous distributed deviating argument, Rad. Mat. 7 (1991), 167–176.Suche in Google Scholar
[27] Zhang, C.—Şenel, M. T.—Li, T.: Oscillation of second-order half-linear differential equations with several neutral terms, J. Appl. Math. Comput. 44 (2014), 511–518.10.1007/s12190-013-0705-xSuche in Google Scholar
[28] Zhao, J. H.—Meng, F. W.: Oscillation criteria for second-order neutral equations with distributed deviating argument, Appl. Math. Comput. 206 (2008), 485–493.10.1016/j.amc.2008.09.021Suche in Google Scholar
© 2016 Mathematical Institute Slovak Academy of Sciences
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