ON OSCILLATORY BEHAVIOUR OF THIRD-ORDER HALF-LINEAR DYNAMIC EQUATIONS ON TIME SCALES

被引：5

作者：

Grace, Said R. ^{[1
]}

Chhatria, Gokula Nanda ^{[2
]}

机构：

[1] Cairo Univ, Dept Engn Math, Fac Engn, Giza 12221, Egypt

[2] Sambalpur Univ, Dept Math, Sambalpur 768019, India

来源：

OPUSCULA MATHEMATICA | 2022年 / 42卷 / 06期

关键词：

oscillation; asymptotic behaviour; dynamic equation on time scales; comparison method; Riccati technique; NEHARI TYPE CRITERIA; DIFFERENTIAL-EQUATIONS; ASYMPTOTIC-BEHAVIOR; HILLE;

D O I：

10.7494/OpMath.2022.42.6.849

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this work, we study the oscillation and asymptotic behaviour of third-order nonlinear dynamic equations on time scales. The findings are obtained using an integral criterion as well as a comparison theorem with the oscillatory properties of a first-order dynamic equation. As a consequence, we give conditions which guarantee that all solutions to the aforementioned problem are only oscillatory, different from any other result in the literature. We propose novel oscillation criteria that improve, extend, and simplify existing ones in the literature. The results are associated with a numerical example. We point out that the results are new even for the case T = R or T = Z.

引用

页码：849 / 865

页数：17

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