Dynamics of Third-Order Nonlinear Neutral Equations

Author:

Wang Hua1,Liu Li1,Tan Yanxiang2

Affiliation:

1. School of Mathematics and Computing Science, Changsha University of Science and Technology, Changsha, Hunan 410114, China

2. College of Mathematics and Econometrics, Hunan University, Changsha, Hunan 410082, China

Abstract

The aim of this paper is to study oscillatory and asymptotic properties of the third-order nonlinear neutral equation with continuously distributed delays of the form(r(t)([xt+abpt,μxτt,μdμ])α)+cdqt,ξfαxgt,ξdξ=0. Applying suitable generalized Riccati transformation and integral averaging technique, we present new criteria for oscillation or certain asymptotic behavior of nonoscillatory solutions of this equation. Obtained results essentially improve and complement earlier ones.

Funder

National Natural Science Foundation of China

Publisher

Hindawi Limited

Subject

Modelling and Simulation

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