Skip to main content
SpringerLink
Log in

Oscillation Criteria for a Class of Third-Order Neutral Dynamic Equations with Distributed Deviating Arguments

  • Conference paper
  • First Online:
Frontier Computing (FC 2018)

Part of the book series: Lecture Notes in Electrical Engineering ((LNEE,volume 542))

Included in the following conference series:

  • 63 Accesses

Abstract

In this paper, the oscillation property for a class of third-order neutral dynamic equations with distributed deviating arguments is studied. Using the generalized Riccati inequality and integral averaging technique, some new oscillation results are established, which show that any solution of the equations will be either oscillatory or convergent to zero. Finally, two examples are given to show that the results are in good agreement with our theoretical analysis.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Grace, S.R., Garwal, R.P., Pavani, R., et al.: On the oscillation of certain third order nonlinear functional differential equations. Appl. Math. Comput. 202(2), 102–112 (2008)

    MathSciNet  MATH  Google Scholar 

  2. Zhang, Q., Gao, L., Yu, Y.: Oscillation criteria of third-order neutral differential equations with continuously delay. Appl. Math. Lett. 25(10), 1514–1519 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  3. Tian, Y., Cai, Y., Fu, Y., et al.: Oscillation and asymptotic behavior of third-order neutral differential equations with distributed deviating arguments. Ade. Differ. Equ-ny. 2015(1), 1–14 (2015)

    Article  MATH  Google Scholar 

  4. Baculikova, B., Dzurina, J.: Oscillation of third-order nonlinear differential equations. Appl. Math. Lett. 24(2), 466–470 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  5. Baculikova, B., Dzurina, J.: Property (A) of third-order advanced differential equations. Math. Slovaca. 64(2), 339–346 (2014)

    Google Scholar 

  6. Yang, L., Xu, Z.: Oscillation of certain third-order quasilinear neutral differential equation. Math. Slovaca. 64(1), 85–100 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  7. Baculikova, B., Dzurina, J.: Oscillation of third-order neutral differential equations. Appl. Math. Model. 52, 215–226 (2010)

    MathSciNet  MATH  Google Scholar 

  8. Bartušek, M., Došlá, Z.: Oscillation of third order differential equation with damping term. Czech. Math. J. 65(2), 301–316 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  9. Wang, Y., Han, Z., Sun, S., et al.: Hille and Nehari-type oscillation criteria for third-order Emden–Fowler neutral delay dynamic equations. B. Malays. Math. Sci. So. 40, 1187–1217 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  10. Shi, Y., Han, Z., Hou, C.: Oscillation criteria for third order neutral Emden-Fowler delay dynamic equations on time scales. Appl. Math. Comput. 55, 175–190 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  11. Baculikova, B., Rani, B., Selvarangam, S., et al.: Properties of Kneser’s solution for half-linear third order neutral differential equations. Acta. Math. Hune. 152(2), 525–533 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  12. Liu, H., Fan, W., Liu, P.: Oscillation and asymptotic analysis on a new generalized Emden Fowler equation. Appl. Math. Comput. 219(5), 2739–2748 (2012)

    MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

This research was supported by the Natural Science of China (11261010), Natural Science.

Foundation of Yunnan Provincial Department of Education (2017ZDX027).

Author information

Authors and Affiliations

  1. School of Mathematics and Statistics, Pu Er University, Pu Er, 665000, China

    Yuanxian Hui

  2. School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang, 471023, China

    Peiluan Li

  3. School of Basic Courses, Guangdong Pharmaceutical University, Guangzhou, 510006, China

    Xunhuan Deng

Authors
  1. Yuanxian Hui
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Peiluan Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Xunhuan Deng
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yuanxian Hui .

Editor information

Editors and Affiliations

  1. Department of Computer Science and Information Engineering, National Taichung University of Science and Technology, Taichung, Taiwan

    Jason C. Hung

  2. School of Computer Science and Engineering, The University of Aizu, Aizu-Wakamatsu, Japan

    Neil Y. Yen

  3. Department of Innovative Information and Technology, Tamkang University, Yilan County, Taiwan

    Lin Hui

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Singapore Pte Ltd.

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Hui, Y., Li, P., Deng, X. (2019). Oscillation Criteria for a Class of Third-Order Neutral Dynamic Equations with Distributed Deviating Arguments. In: Hung, J., Yen, N., Hui, L. (eds) Frontier Computing. FC 2018. Lecture Notes in Electrical Engineering, vol 542. Springer, Singapore. https://doi.org/10.1007/978-981-13-3648-5_101

Download citation

Publish with us

Policies and ethics

Search

Navigation