Abstract
The oscillation of a class of neutral third-order semi-linear differential equations is studied. The Riccati transform technique is used to construct different functions and classical inequalities. Some new oscillation theories of differential equations are established. Our results differ from the results in other literature, and use examples to illustrate the application of the conclusions.
Highlights
Consider the oscillation of a class of third-order semilinear neutral delay differential equations of the form (E)Assume the following conditions hold (A1) p(t), q(t) C t0, 0,0 p(t) p 1, q(t) 0; ( A2 )1 r (s)ds ; t0 tAccording to the custom, the solution of the equation is called oscillatory, if it has arbitrarily large zeros; otherwise it is said to be non- oscillatory
Our results differ from the results in other literature, and use examples to illustrate the application of the conclusions
In 2017, Hui Yuanxian et al Established a number of new oscillate criteria to guarantee that all solutions of the equation http://jmr.ccsenet.org Journal of Mathematics Research
Summary
Assume the following conditions hold (A1) p(t), q(t) C t0, , 0, ,0 p(t) p 1, q(t) 0;. The solution of the equation is called oscillatory, if it has arbitrarily large zeros; otherwise it is said to be non- oscillatory. H, 2015) for second-order semi-linear neutral differential equations (r(t) Z (t) 1 Z (t)) q(t) x( (t)) 1 x( (t)) 0. N-depth research was done to give some new oscillate criteria. In the past few years, the research on the vibration of third-order semi-linear differential equations has begun to attract attention, but its research results on oscillations are still relatively small, such as references(LI, Y. In 2017, Hui Yuanxian et al Established a number of new oscillate criteria to guarantee that all solutions of the equation http://jmr.ccsenet.org
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