Oscillation of nonlinear second-order neutral delay differential equations
-
2218
Downloads
-
3524
Views
Authors
Jiashan Yang
- School of Information and Electronic Engineering, Wuzhou University, Wuzhou, Guangxi 543002, P. R. China.
Jingjing Wang
- School of Information Science & Technology, Qingdao University of Science & Technology, Qingdao, Shandong 266061, P. R. China.
Xuewen Qin
- School of Information and Electronic Engineering, Wuzhou University, Wuzhou, Guangxi 543002, P. R. China.
Tongxing Li
- LinDa Institute of Shandong Provincial Key Laboratory of Network Based Intelligent Computing, Linyi University, Linyi, Shandong 276005, P. R. China.
- School of Informatics, Linyi University, Linyi, Shandong 276005, P. R. China.
Abstract
By using a couple of Riccati substitutions, we establish several new oscillation criteria for a class of second-order nonlinear
neutral delay differential equations. These results complement and improve the related contributions reported in the literature.
Share and Cite
ISRP Style
Jiashan Yang, Jingjing Wang, Xuewen Qin, Tongxing Li, Oscillation of nonlinear second-order neutral delay differential equations, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 5, 2727--2734
AMA Style
Yang Jiashan, Wang Jingjing, Qin Xuewen, Li Tongxing, Oscillation of nonlinear second-order neutral delay differential equations. J. Nonlinear Sci. Appl. (2017); 10(5):2727--2734
Chicago/Turabian Style
Yang, Jiashan, Wang, Jingjing, Qin, Xuewen, Li, Tongxing. "Oscillation of nonlinear second-order neutral delay differential equations." Journal of Nonlinear Sciences and Applications, 10, no. 5 (2017): 2727--2734
Keywords
- Oscillation
- neutral differential equation
- nonlinear equation
- delayed argument
- Riccati substitution.
References
-
[1]
R. P. Agarwal, M. Bohner, W.-T. Li, Nonoscillation and oscillation: theory for functional differential equations, Monographs and Textbooks in Pure and Applied Mathematics, Marcel Dekker, Inc., New York (2004)
-
[2]
R. P. Agarwal, M. Bohner, T.-X. Li, C.-H. Zhang, A new approach in the study of oscillatory behavior of even-order neutral delay differential equations, Appl. Math. Comput., 225 (2013), 787–794.
-
[3]
R. P. Agarwal, M. Bohner, T.-X. Li, C.-H. Zhang, Oscillation of second-order differential equations with a sublinear neutral term, Carpathian J. Math., 30 (2014), 1–6.
-
[4]
R. P. Agarwal, M. Bohner, T.-X. Li, C.-H. Zhang, Oscillation of second-order Emden–Fowler neutral delay differential equations, Ann. Mat. Pura Appl., 193 (2014), 1861–1875.
-
[5]
R. P. Agarwal, C.-H. Zhang, T.-X. Li, Some remarks on oscillation of second order neutral differential equations, Appl. Math. Comput., 274 (2016), 178–181.
-
[6]
B. Baculíková, J. Džurina, Oscillation theorems for second order neutral differential equations, Comput. Math. Appl. , 61 (2011), 94–99.
-
[7]
B. Baculíková, J. Džurina, Oscillation theorems for second-order nonlinear neutral differential equations, Comput. Math. Appl., 62 (2011), 4472–4478.
-
[8]
B. Baculíková, T.-X. Li, J. Džurina, Oscillation theorems for second-order superlinear neutral differential equations, Math. Slovaca, 63 (2013), 123–134.
-
[9]
Z.-L. Han, T.-X. Li, S.-R. Sun, Y.-B. Sun, Remarks on the paper [Appl. Math. Comput. 207 (2009) 388–396], Appl. Math. Comput., 215 (2010), 3998–4007.
-
[10]
M. Hasanbulli, Yu. V. Rogovchenko, Oscillation criteria for second order nonlinear neutral differential equations, Appl. Math. Comput., 215 (2010), 4392–4399.
-
[11]
T.-X. Li, R. P. Agarwal, M. Bohner, Some oscillation results for second-order neutral dynamic equations, Hacet. J. Math. Stat., 41 (2012), 715–721.
-
[12]
T.-X. Li, Yu. V. Rogovchenko, Oscillatory behavior of second-order nonlinear neutral differential equations, Abstr. Appl. Anal., 2014 (2014), 8 pages.
-
[13]
T.-X. Li, Yu. V. Rogovchenko, Oscillation theorems for second-order nonlinear neutral delay differential equations, Abstr. Appl. Anal., 2014 (2014), 5 pages.
-
[14]
T.-X. Li, Yu. V. Rogovchenko, Oscillation of second-order neutral differential equations, Math. Nachr., 288 (2015), 1150– 1162.
-
[15]
T.-X. Li, Yu. V. Rogovchenko, Oscillation criteria for even-order neutral differential equations, Appl. Math. Lett., 61 (2016), 35–41.
-
[16]
T.-X. Li, Yu. V. Rogovchenko, C.-H. Zhang, Oscillation of second-order neutral differential equations, Funkcial. Ekvac., 56 (2013), 111–120.
-
[17]
T.-X. Li, Yu. V. Rogovchenko, C.-H. Zhang, Oscillation results for second-order nonlinear neutral differential equations, Adv. Difference Equ., 2013 (2013), 13 pages.
-
[18]
F.-W. Meng, R. Xu, Kamenev-type oscillation criteria for even order neutral differential equations with deviating arguments, Appl. Math. Comput., 190 (2007), 1402–1408.
-
[19]
F.-W. Meng, R. Xu, Oscillation criteria for certain even order quasi-linear neutral differential equations with deviating arguments, Appl. Math. Comput., 190 (2007), 458–464.
-
[20]
X.-L. Wang, F.-W. Meng, Oscillation criteria of second-order quasi-linear neutral delay differential equations, Math. Comput. Modelling, 46 (2007), 415–421.
-
[21]
G.-J. Xing, T.-X. Li, C.-H. Zhang, Oscillation of higher-order quasi-linear neutral differential equations, Adv. Difference Equ., 2011 (2011), 10 pages.
-
[22]
R. Xu, F.-W. Meng, New Kamenev-type oscillation criteria for second order neutral nonlinear differential equations, Appl. Math. Comput., 188 (2007), 1364–1370.
-
[23]
R. Xu, F.-W. Meng, Oscillation criteria for second order quasi-linear neutral delay differential equations, Appl. Math. Comput., 192 (2007), 216–222.
-
[24]
J.-S. Yang, X.-W. Qin, Oscillation criteria for certain second-order Emden–Fowler delay functional dynamic equations with damping on time scales, Adv. Difference Equ., 2015 (2015), 16 pages.
-
[25]
L.-H. Ye, Z.-T. Xu, Oscillation criteria for second order quasilinear neutral delay differential equations, Appl. Math. Comput, 207 (2009), 388–396.
-
[26]
C.-H. Zhang, R. P. Agarwal, M. Bohner, T.-X. Li, New oscillation results for second-order neutral delay dynamic equations, Adv. Difference Equ., 2012 (2012), 14 pages.
-
[27]
J.-H. Zhao, F.-W. Meng, Oscillation criteria for second-order neutral equations with distributed deviating argument, Appl. Math. Comput., 206 (2008), 485–493.
-
[28]
J.-C. Zhong, Z.-G. Ouyang, S.-L. Zou, An oscillation theorem for a class of second-order forced neutral delay differential equations with mixed nonlinearities, Appl. Math. Lett., 24 (2011), 1449–1454.