Abstract
In this paper, we present oscillation criteria for the second-order nonlinear dynamic equation \({[a(t)\phi_{\gamma} (x^{\Delta}(t))]^{\Delta} + p(t)\phi_{\gamma}(x^{\Delta^{\sigma}}(t)) + q_{0}(t) \phi_{\gamma}(x(g_{0}(t)))+\sum_{i=1}^{2}\int_{a_{i}}^{b_{i}}q_{i}(t,s)\phi_{\alpha_{i}(s)}(x(g_{i}(t,s))) \Delta \zeta_{i}(s)=0}\) on a time scale \({\mathbb{T}}\) which is unbounded above. Our results generalize and improve some known results for oscillation of second-order nonlinear dynamic equation. Some examples are given to illustrate the main results.
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El-Shobaky, E., Elabbasy, E.M., Hassan, T.S. et al. Oscillation Criteria for Functional Nonlinear Dynamic Equations with \({\gamma}\) -Laplacian, Damping and Nonlinearities Given by Riemann–Stieltjes Integrals. Mediterr. J. Math. 13, 981–1003 (2016). https://doi.org/10.1007/s00009-015-0553-z
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DOI: https://doi.org/10.1007/s00009-015-0553-z