Abstract
This paper is concerned with the oscillatory properties of even order advanced type dynamic equation with mixed nonlinearities of the form
on an arbitrary time scale \(\mathbb{T}\), where Φ ∗(u)=|u|∗−1 u. We present some new oscillation criteria for the equation by introducing parameter functions, establishing a new lemma, using a Hardy-Littlewood-Pólya inequality and an arithmetic-geometric mean inequality and developing a generalized Riccati technique. Our results extend and supplement some known results in the literature. Several examples are given to illustrate our main results.
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Acknowledgements
This work was supported by the National Natural Science Foundation of P.R. China (Grant No. 11271311) and the Natural Science Foundation of Hunan of P.R. China (Grant No. 11JJ3010).
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Chen, DX., Qu, PX. Oscillation of even order advanced type dynamic equations with mixed nonlinearities on time scales. J. Appl. Math. Comput. 44, 357–377 (2014). https://doi.org/10.1007/s12190-013-0697-6
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DOI: https://doi.org/10.1007/s12190-013-0697-6