On oscillatory behaviour of third-order half-linear dynamic equations on time scales

Opuscula Mathematica

article

Said R. Grace¹  Gokula Nanda Chhatria (corresponding author)² 

[1] Cairo University, Department of Engineering Mathematics, Faculty of Engineering;Sambalpur University, Department of Mathematics

关键词: oscillation;    asymptotic behaviour;    dynamic equation on time scales;    comparison method;    Riccati technique.;   

DOI  :  10.7494/OpMath.2022.42.6.849

学科分类：环境科学（综合）

来源: AGH University of Science and Technology Press

【 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 \(\mathbb{T}=\mathbb{R}\) or \(\mathbb{T}=\mathbb{Z}\).

【 授权许可】

CC BY-NC