Existence of nonoscillatory solutions to third-order neutral functional dynamic equations on time scales
Volume 11, Issue 2, pp 274--287
http://dx.doi.org/10.22436/jnsa.011.02.09
Publication Date: February 07, 2018
Submission Date: September 18, 2017
Revision Date: October 19, 2017
Accteptance Date: January 11, 2018
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Authors
Yang-Cong Qiu
- School of Humanities and Social Science, Shunde Polytechnic, Foshan, Guangdong 528333, P. R. China.
Haixia Wang
- School of Economics, Ocean University of China, Qingdao, Shandong 266100, P. R. China.
Cuimei Jiang
- cSchool of Science, Qilu University of Technology, Jinan, Shandong 250353, P. R. China.
- College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao, Shandong 266590, P. R. China.
Tongxing Li
- School of Information Science and Engineering, Linyi University, Linyi, Shandong 276005, P. R. China.
- School of Control Science and Engineering, Shandong University, Jinan, Shandong 250061, P. R. China.
Abstract
By employing Krasnoselskii's fixed point theorem, we
establish the existence of nonoscillatory solutions to a class of
third-order neutral functional dynamic equations on time scales. In
addition, the significance of the results is illustrated by three
examples.
Share and Cite
ISRP Style
Yang-Cong Qiu, Haixia Wang, Cuimei Jiang, Tongxing Li, Existence of nonoscillatory solutions to third-order neutral functional dynamic equations on time scales, Journal of Nonlinear Sciences and Applications, 11 (2018), no. 2, 274--287
AMA Style
Qiu Yang-Cong, Wang Haixia, Jiang Cuimei, Li Tongxing, Existence of nonoscillatory solutions to third-order neutral functional dynamic equations on time scales. J. Nonlinear Sci. Appl. (2018); 11(2):274--287
Chicago/Turabian Style
Qiu, Yang-Cong, Wang, Haixia, Jiang, Cuimei, Li, Tongxing. "Existence of nonoscillatory solutions to third-order neutral functional dynamic equations on time scales." Journal of Nonlinear Sciences and Applications, 11, no. 2 (2018): 274--287
Keywords
- Nonoscillatory solution
- neutral dynamic equation
- third-order
- time scale
MSC
References
-
[1]
R. P. Agarwal, M. Bohner, Basic calculus on time scales and some of its applications , Results Math., 35 (1999), 3–22.
-
[2]
R. P. Agarwal, M. Bohner, T.-X. Li, C.-H. Zhang , Hille and Nehari type criteria for third-order delay dynamic equations, J. Difference Equ. Appl., 19 (2013), 1563–1579.
-
[3]
R. P. Agarwal, M. Bohner, T.-X. Li, C.-H. Zhang , A Philos-type theorem for third-order nonlinear retarded dynamic equations, Appl. Math. Comput., 249 (2014), 527–531.
-
[4]
R. P. Agarwal, M. Bohner, D. O’Regan, A. Peterson , Dynamic equations on time scales: a survey, J. Comput. Appl. Math., 141 (2002), 1–26.
-
[5]
R. P. Agarwal, M. Bohner, S.-H. Tang, T.-X. Li, C.-H. Zhang , Oscillation and asymptotic behavior of third-order nonlinear retarded dynamic equations, Appl. Math. Comput., 219 (2012), 3600–3609.
-
[6]
E. Akın, T. S. Hassan, Comparison criteria for third order functional dynamic equations with mixed nonlinearities, Appl. Math. Comput., 268 (2015), 169–185.
-
[7]
M. Bohner, A. Peterson , Dynamic equations on time scales, An introduction with applications, Birkhäuser Boston, Boston (2001)
-
[8]
M. Bohner, A. Peterson, Advances in dynamic equations on time scales, Birkhäuser Boston, Boston (2003)
-
[9]
Y.-S. Chen , Existence of nonoscillatory solutions of nth order neutral delay differential equations, Funkcial. Ekvac., 35 (1992), 557–570.
-
[10]
X.-H. Deng, Q.-R. Wang, Nonoscillatory solutions to second-order neutral functional dynamic equations on time scales , Commun. Appl. Anal., 18 (2014), 261–280.
-
[11]
L. H. Erbe, Q.-K. Kong, B. G. Zhang , Oscillation theory for functional differential equations, Marcel Dekker, New York (1995)
-
[12]
J. Gao, Q.-R. Wang , Existence of nonoscillatory solutions to second-order nonlinear neutral dynamic equations on time scales, Rocky Mountain J. Math., 43 (2013), 1521–1535.
-
[13]
T. S. Hassan, Oscillation of third order nonlinear delay dynamic equations on time scales, Math. Comput. Modelling, 49 (2009), 1573–1586.
-
[14]
T. S. Hassan, R. P. Agarwal, W. W. Mohammed , Oscillation criteria for third-order functional half-linear dynamic equations, Adv. Difference Equ., 2017 (2017), 28 pages.
-
[15]
S. Hilger , Ein Maßkettenkalkül mit Anwendung auf Zentrumsmannigfaltigkeiten, Ph.D. thesis, Universität Würzburg, Würzburg, Germany (1988)
-
[16]
S. Hilger, Analysis on measure chains–a unified approach to continuous and discrete calculus, Results Math., 18 (1990), 18–56.
-
[17]
T.-X. Li, Z.-L. Han, S.-R. Sun, D.-W. Yang , Existence of nonoscillatory solutions to second-order neutral delay dynamic equations on time scales, Adv. Difference Equ., 2009 (2009 ), 10 pages.
-
[18]
T.-X. Li, Z.-L. Han, S.-R. Sun, Y.-G. Zhao, Oscillation results for third order nonlinear delay dynamic equations on time scales, Bull. Malays. Math. Sci. Soc., 34 (2011), 639–648.
-
[19]
R. M. Mathsen, Q.-R.Wang, H.-W.Wu , Oscillation for neutral dynamic functional equations on time scales, J. Difference Equ. Appl., 10 (2004), 651–659.
-
[20]
Y.-C. Qiu, Nonoscillatory solutions to third-order neutral dynamic equations on time scales, Adv. Difference Equ., 2014 (2014 ), 25 pages.
-
[21]
Y.-C. Qiu, Q.-R. Wang , Existence of nonoscillatory solutions to higher-order nonlinear neutral dynamic equations on time scales, Bull. Malays. Math. Sci. Soc., 2016 (2016 ), 18 pages.
-
[22]
Y.-C. Qiu, A. Zada, H.-Y. Qin, T.-X. Li , Oscillation criteria for nonlinear third-order neutral dynamic equations with damping on time scales, J. Funct. Spaces, 2017 (2017 ), 8 pages.
-
[23]
Y.-C. Qiu, A. Zada, S.-H. Tang, T.-X. Li, Existence of nonoscillatory solutions to nonlinear third-order neutral dynamic equations on time scales , J. Nonlinear Sci. Appl., 10 (2017), 4352–4363.
-
[24]
Z.-Q. Zhu, Q.-R. Wang , Existence of nonoscillatory solutions to neutral dynamic equations on time scales, J. Math. Anal. Appl., 335 (2007), 751–762.