Existence of nonoscillatory solutions to higher-order nonlinear neutral dynamic equations on time scales. (English) Zbl 1406.34110
Summary: In this paper, we establish the existence of nonoscillatory solutions to a class of higher-order nonlinear neutral dynamic equations on time scales by employing Kranoselskii’s fixed point theorem. In addition, two examples are included to illustrate the significance of the results.
MSC:
| 34N05 | Dynamic equations on time scales or measure chains |
| 34C10 | Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations |
Keywords:
higher-order nonlinear neutral dynamic equations; time scales; existence; nonoscillatory solutions; Kranoselskii’s fixed point theoremReferences:
| [1] | Hilger, S: Ein Maßkettenkalkül mit Anwendung auf Zentrumsmannigfaltigkeiten. Ph.D. thesis. Universität Würzburg (1988) · Zbl 0695.34001 |
| [2] | Hilger, S.: Analysis on measure chain—a unified approach to continuous and discrete calculus. Results Math. 18, 18-56 (1990) · Zbl 0722.39001 · doi:10.1007/BF03323153 |
| [3] | Agarwal, R.P., Bohner, M.: Basic calculus on time scales and some of its applications. Results Math. 35, 3-22 (1999) · Zbl 0927.39003 · doi:10.1007/BF03322019 |
| [4] | Agarwal, R.P., Bohner, M., O’Regan, D., Peterson, A.: Dynamic equations on time scales: a survey. J. Comput. Appl. Math. 141, 1-26 (2002) · Zbl 1020.39008 · doi:10.1016/S0377-0427(01)00432-0 |
| [5] | Bohner, M., Peterson, A.: Dynamic Equations on Time Scales: An Introduction with Applications. Birkhäuser, Boston (2001) · Zbl 0978.39001 · doi:10.1007/978-1-4612-0201-1 |
| [6] | Bohner, M., Peterson, A. (eds.): Advances in Dynamic Equations on Time Scales. Birkhäuser, Boston (2003) · Zbl 1025.34001 |
| [7] | Chen, Y.S.: Existence of nonoscillatory solutions of \[n\] nth order neutral delay differential equations. Funcialaj Ekvacioj 35, 557-570 (1992) · Zbl 0787.34056 |
| [8] | Erbe, L.H., Kong, Q.K., Zhang, B.G.: Oscillation Theory for Functional-Differential Equations. Monographs and Textbooks in Pure and Applied Mathematics, vol. 190. Marcel Dekker, New York (1995) · Zbl 0821.34067 |
| [9] | Zhu, Z.Q., Wang, Q.R.: Existence of nonoscillatory solutions to neutral dynamic equations on time scales. J. Math. Anal. Appl. 335, 751-762 (2007) · Zbl 1128.34043 · doi:10.1016/j.jmaa.2007.02.008 |
| [10] | Zhu, S.L., Lian, F.Y.: Existence for nonoscillatory solutions of forced higher-order nonlinear neutral dynamic equations. Dyn. Contin. Discret. Impuls. Syst. Ser. A 20, 179-196 (2013) · Zbl 1268.34194 |
| [11] | Gao, J., Wang, Q.R.: Existence of nonoscillatory solutions to second-order nonlinear neutral dynamic equations on time scales. Rocky Mt. J. Math. 43, 1521-1535 (2013) · Zbl 1287.34083 · doi:10.1216/RMJ-2013-43-5-1521 |
| [12] | Deng, X.H., Wang, Q.R.: Nonoscillatory solutions to second-order neutral functional dynamic equations on time scales. Commun. Appl. Anal. 18, 261-280 (2014) · Zbl 1343.34206 |
| [13] | Qiu, Y.C.: Nonoscillatory solutions to third-order neutral dynamic equations on time scales. Adv. Diff. Equ. 2014, 309 (2014) · Zbl 1347.34138 · doi:10.1186/1687-1847-2014-309 |
| [14] | Tao, C.Y., Sun, T.X., Xi, H.J.: Existence of the nonoscillatory solutions of higher order neutral dynamic equations on time scales. Adv. Diff. Equ. 2015, 279 (2015) · Zbl 1351.34109 · doi:10.1186/s13662-015-0621-5 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
