Some oscillation criteria for second-order delay dynamic equations (Q2867532)

The oscillation of the second-order delay dynamic equation NEWLINE\[NEWLINE [p(t)y^\Delta]^\Delta+f(t,y^\sigma(t),y(\tau_1(t)),\dots,y(\tau_n(t)))=0, \quad t\in[t_0,\infty)\cap\mathbb T, NEWLINE\]NEWLINE is studied under the assumptions \(f(t,u,v_1,\dots,v_n)=-f(t,-u,-v_1,\dots,-v_n)\); \(f>0\) for \(u,v_1,\dots,v_n>0\), \(t\in\mathbb T\); \(f\) is nondecreasing in \(v_i\), \(1\leq i\leq n\), and \(u\) for all \(t\in\mathbb T\), \(u,v_1,\dots,v_n>0\); the delay functions \(\tau_i:\mathbb T\to\mathbb T\) are right-dense continuous and satisfy \(\tau_i(t)\leq t\leq\sigma(t)\), \(t\in\mathbb T\), and \(\lim_{t\to\infty}(t)=\infty\).NEWLINENEWLINE The obtained results extend known results for the oscillation of second-order differential equations that have been established by \textit{L. Erbe} [Can. Math. Bull. 16, 49--56 (1973; Zbl 0272.34095)].