Nonlinear oscillation of certain third-order neutral differential equation with distributed delay

Document Type : Research Paper

Authors

1 Paavai Engineering College (Autonomous) Paavai Institutions, Paavai Nagar, NH-7, Pachal -637 018. Namakkal Dist. Tamilnadu, India.

2 Department of Mathematics, Aringar Anna Government Arts College, Namakkal-637002, Tamilnadu, India.

3 Deputy Directorate of statistics, Government of Tamil Nadu, Namakkal-637003, Tamil Nadu, India.

4 Department of Mathematics, Faculty of Science, Mansoura University, Mansoura, 35516, Egypt.

Abstract

The authors obtain necessary and sufficient conditions for the existence of oscillatory solutions with a specified asymptotic behavior of solutions to a nonlinear neutral differential equation with distributed delay of third order. We give new theorems which ensure that every solution to be either oscillatory or converges to zero asymptotically. Examples dwelling upon the importance of applicability of these results.

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Journal of Mahani Mathematical Research
Volume 7, Issue 1
March 2018
Pages 1-12

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History

  • Receive Date: 18 November 2017
  • Revise Date: 01 March 2018
  • Accept Date: 10 March 2018

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