Title: Oscillation of second-order nonlinear delay dynamic equations on time scales with a nonpositive neutral term

Authors: H.A. Agwa; A.M.M. Khodier; M. Hamam

Addresses: Faculty of Education, Department of Mathematics, Ain Shams University, Roxy, Cairo, 11341, Egypt ' Faculty of Education, Department of Mathematics, Ain Shams University, Roxy, Cairo, 11341, Egypt ' Faculty of Education, Department of Mathematics, Ain Shams University, Roxy, Cairo, 11341, Egypt

Abstract: In this paper, we establish some new oscillation criteria for second- order nonlinear neutral delay dynamic equation of the form (r(t)((m(t)y(t) ? p(t)y(τ(t)))^∆)^γ )^∆ + ƒ (t, y(?(t))) = 0 on a time scale 𝕋. The obtained results not only generalise and extend some existing results but also can be applied to some of oscillation problems that are not covered before. Finally, we give an example to illustrate our main results.

Keywords: oscillation; neutral equation; delay equation; dynamic equation; time scale.

DOI: 10.1504/IJDSDE.2022.128121

International Journal of Dynamical Systems and Differential Equations, 2022 Vol.12 No.6, pp.477 - 492

Accepted: 24 Nov 2021
Published online: 06 Jan 2023 *

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