Oscillation of Second-Order Half-Linear Neutral Advanced Differential Equations

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  • School of Mathematical Sciences, University of Jinan, Jinan 250022, China

Received date: 2019-09-18

  Revised date: 2020-07-25

  Online published: 2021-09-16

Supported by

This research is supported by the Shandong Provincial Natural Science Foundation of China (ZR2017MA043).

Abstract

The purpose of this paper is to study the oscillation of second-order half-linear neutral differential equations with advanced argument of the form
(r(t)((y(t) + p(t)y(τ(t)))')α)' + q(t)yα(σ(t))=0, tt0,
when ${r^{-\frac{1}{\alpha }}}$(s)ds < ∞. We obtain sufficient conditions for the oscillation of the studied equations by the inequality principle and the Riccati transformation. An example is provided to illustrate the results.

Cite this article

Shan Shi, Zhenlai Han . Oscillation of Second-Order Half-Linear Neutral Advanced Differential Equations[J]. Communications on Applied Mathematics and Computation, 2021 , 3(3) : 497 -508 . DOI: 10.1007/s42967-020-00092-4

References

1. Agarwal, R.P., Bohner, M., Li, T., Zhang, C.:Oscillation criteria for second-order dynamic equations on time scales. Appl. Math. Lett. 31, 34-40 (2014)
2. Baculíková, B., Džurina, J.:Oscillation theorems for second order neutral differential equations. Comput. Math. Appl. 61(1), 94-99 (2011)
3. Chatzarakis, G.E., Džurina, J., Jadlovská, I.:New oscillation criteria for second-order half-linear advanced differential equations. Appl. Math. Comput. 347, 404-416 (2019)
4. Džurina, J.:Oscillation theorems for second order advanced neutral differential equations. Tatra Mt. Math. Publ. 48(1), 61-71 (2011)
5. Džurina, J.:Oscillation of the second order advanced differential equations. Electron. J. Qual. Theory Diff. Equ. 20, 1-9 (2018)
6. Elabbasy, E.M., Hassan, T.S., Moaaz, O.:Oscillation behavior of second order nonlinear neutral differential equations with deviating arguments. Opuscula Math. 32(4), 719-730 (2012)
7. Erbe, L., Hassan, T.S., Peterson, A.:Oscillation of second order neutral delay differential equations. Adv. Dyn. Syst. Appl. 3(1), 53-71 (2008)
8. Erbe, L., Hassan, T.S., Peterson, A.:Oscillation criteria for nonlinear functional neutral dynamic equations on time scales. J. Differ. Equ. Appl. 15(11/12), 1097-1116 (2009)
9. Feng, L., Han, Z.:The distribution of generalized zeros of oscillatory solutions for second order nonlinear neutral delay difference equations. Adv. Diff. Equ. 282, 1-15 (2019)
10. Fite, W.B.:Properties of the solutions of certain functional-differential equations. Trans. Am. Math. Soc. 22(3), 311-319 (1921)
11. Hassan, T.S.:Kamenev-type oscillation criteria for second order nonlinear dynamic equations on time scales. Appl. Math. Comput. 217(12), 5285-5297 (2011)
12. Hassan, T.S.:Oscillation criteria for half-linear dynamic equations on time scales. J. Math. Anal. Appl. 45(1), 176-185 (2018)
13. Jadlovská, I.:Iterative oscillation results for second-order differential equations with advanced argument. Electron. J. Diff. Equ. 2017(162), 1-11 (2017)
14. Ladde, G.S., Lakshmikantham, V., Zhang, B.G.:Oscillation theory of differential equations with deviating arguments. In:Dekker M. (ed) Monographs and Textbooks in Pure and Applied Mathematics, New York (1987)
15. Li, H., Sun, S.:Nonoscillation of higher order mixed differential equations with distributed delays. Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas 113(3), 2617-2625 (2019)
16. Li, H., Han, Z., Sun, S.:The distribution of zeros of oscillatory solutions for second order nonlinear neutral delay differential equations. Appl. Math. Lett. 63, 14-20 (2017)
17. Trench, W.F.:Canonical forms and principal systems for general disconjugate equations. Trans. Am. Math. Soc. 189, 319-327 (1974)
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