Abstract
In this paper, we deal with the asymptotics and oscillation of the solutions of fourth-order neutral differential equations of the form r t z ‴ t α ′ + q t x α g t = 0 , where z t : = x t + p t x δ t . By using a generalized Riccati transformation, we study asymptotic behavior and derive some new oscillation criteria. Our results extend and improve some well-known results which were published recently in the literature. Symmetry ideas are often invisible in these studies, but they help us decide the right way to study them, and to show us the correct direction for future developments. An example is given to illustrate the importance of our results.
Highlights
The oscillatory behavior of the solutions to differential equations has been discussed in many papers
The asymptotic behavior of the solutions to delay and neutral delay differential equations were discussed in many works, and there have been very fruitful achievements see [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28]
Our focus is on improving the criteria of oscillation of fourth-order neutral equations r (t) z000 (t)
Summary
The oscillatory behavior of the solutions to differential equations has been discussed in many papers. There are many papers about the oscillation of the solutions to functional differential equations. The asymptotic behavior of the solutions to delay and neutral delay differential equations were discussed in many works, and there have been very fruitful achievements see [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28]. An example is provided to illustrate the main results
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