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Kamenev-type oscillation criteria for higher order nonlinear dynamic equations on time scales

In this paper, we investigate the oscillation of the following higher order dynamic equation $$\{r_n(t)[(r_{n-1}(t)(\cdots(r_1(t)x^\triangle(t))^\triangle\cdots)^\triangle)^\triangle]^\gamma\}^\triangle +F(t,x(\tau(t)))=0$$ on an arbitrary time scale $\bf T$, where $n\geq 2$, $\frac{1}{r_{k}(t)}\ (1\leq k\leq n)$ are positive rd-continuous functions on $\bf T$, and $\gamma$ is the quotient of two odd positive integers, $\tau:\bf T\longrightarrow\bf T$ with $\tau(t)> t$ and $F\in C(\bf T\times \bf R,\bf R)$. We give sufficient conditions under which every solution of this equation is either oscillatory or tends to zero.zero.



Real Time Impact Factor: 2.7

Author Name: Xin Wu, Taixiang Sun, Hongjian Xi, Changhong Chen

URL: View PDF

Keywords: 16871847

ISSN: 16871847

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