On oscillation of a certain class of third-order nonlinear functional dynamic equations on time scales (Q2919575)

Some sufficient conditions are estabished for the third-order nonlinear functional dynamic equation NEWLINE\[NEWLINE(p(t)[(r(t)x^\Delta(t))^\Delta]^\gamma)^\Delta +q(t)f(x(\tau(t)))=0,NEWLINE\]NEWLINE to be oscillatory for \(t\in[t_0,\infty)_{\mathbb T}\) on a time scale \(\mathbb T\), where \(\gamma>0\) is the quotient of odd positive integers, \(p,q,r,\tau\) are positive rd-continuous functions on \(\mathbb T\) and \(f\in C(\mathbb R,\mathbb R)\), \(uf(u)>0\) and \(f(u)/u^\gamma\geq K>0\) for \(u\neq 0\). Results of the paper are obtained by employing the Riccati substitution and the Pötzsche chain rule.