AIMS Mathematics, 2020, 5(4): 3851-3874. doi: 10.3934/math.2020250

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Asymptotic behavior of solutions of third-order neutral differential equations with discrete and distributed delay

1 Department of Mathematics, Paavai Engineering College (Autonomous), Namakkal-637 018, Tamil Nadu, India
2 PG and Research Department of Mathematics, Aringar Anna Government Arts College, Namakkal-637 002, Tamil Nadu, India

By refining the standard Riccati substitution technique, integral averaging technique and comparison principle, we obtain new oscillation and asymptotic behavior for a class of third-order neutral differential equations with discrete and distributed delay. These criteria dealing with some cases have not been covered by the existing results in the literature. We present many sufficient conditions and related examples in order to illustrate the main results.
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