Opuscula Mathematica
Opuscula Math. 42, no. 6 (2022), 849-865

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

Said R. Grace
Gokula Nanda Chhatria
Abstract. 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 \(\mathbb{T}=\mathbb{Z}\).
Keywords: oscillation, asymptotic behaviour, dynamic equation on time scales, comparison method, Riccati technique.
Mathematics Subject Classification: 34C10, 34K11, 34N05, 39A10.
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About the authors ▼
Said R. Grace
https://orcid.org/0000-0001-8783-5227
Cairo University, Department of Engineering Mathematics, Faculty of Engineering, Orman, Giza 12221, Egypt
Gokula Nanda Chhatria (corresponding author)
https://orcid.org/0000-0002-2092-6420
Sambalpur University, Department of Mathematics, Sambalpur-768019, India
About the article ▼
Communicated by Josef Diblík.
Received: 2022-06-23.
Revised: 2022-08-03.
Accepted: 2022-08-03.
Published online: 2022-11-24.
Cite this article as ▼
Said R. Grace, Gokula Nanda Chhatria, On oscillatory behaviour of third-order half-linear dynamic equations on time scales, Opuscula Math. 42, no. 6 (2022), 849-865, https://doi.org/10.7494/OpMath.2022.42.6.849.
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