Oscillation criteria for higher order quasilinear dynamic equations with Laplacians and a deviating argument | ||||
Journal of the Egyptian Mathematical Society | ||||
Volume 25, Issue 2, 2017, Page 178-185 PDF (436.24 K) | ||||
DOI: 10.1016/j.joems.2016.09.003 | ||||
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Abstract | ||||
In this paper, we deal with the oscillation of the solutions of the higher order quasilinear dynamic equation with Laplacians and a deviating argument in the form of (x[n−1] )(t) + p(t)φγ (x(g(t))) = 0 on an above-unbounded time scale, where n ≥ 2, x[i] (t) := ri(t)φαi x[i−1] (t) , i = 1, 2, . . ., n − 1, with x[0] = x. By using a generalized Riccati transformation and integral averaging technique, we establish some new oscillation criteria for the cases when n is even and odd, and when α > γ , α = γ , and α < γ , respectively, with α = α1 ···αn−1 and without any restrictions on the time scale. | ||||
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