Opuscula Math. 42, no. 6 (2022), 849-865
https://doi.org/10.7494/OpMath.2022.42.6.849

 
Opuscula Mathematica

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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  • Communicated by Josef Diblík.
  • Received: 2022-06-23.
  • Revised: 2022-08-03.
  • Accepted: 2022-08-03.
  • Published online: 2022-11-24.
Opuscula Mathematica - cover

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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