Oscillation for higher order dynamic equations on time scales (Q2015291)

Summary: We investigate the oscillation of the following higher order dynamic equation \[ \{a_n(t)[(a_{n-1}(t)(\cdots(a_1(t)x^\Delta(t))^\Delta \cdots)^\Delta)^\Delta]^\alpha\}^\Delta + p(t)x^\beta(t)=0 \] on some time scale \(\mathbf{T}\), where \(n\geq 2\), \(a_k(t) (1\leq k\leq n)\) and \(p(t)\) are positive rd-continuous functions on \(\mathbf{T}\) and \(\alpha\), \(\beta\) are the quotient of odd positive integers. We give sufficient conditions under which every solution of this equation is either oscillatory or tends to zero.