Comparison theorems and applications of oscillation of neutral differential equations (Q1177981)

The author studies comparison theorems for neutral delay differential equations \[ {d^ n \over dt^ n} [x(t)-P(t)x(t-\tau)]+(- 1)^{n+1}\sum_{i=0}^ k Q_ i(t)f_ i(x(t-\sigma_ i(t)))=0, \] where \(n\geq 1\), \(\tau>0\) is a constant; \(P,Q_ i,\sigma_ i\in C([t_ 0,\infty),[0,\infty))\), \(\lim_{t\to\infty}(t-\sigma_ i(t))=\infty\), \(i=0,1,\dots,k\) and there exists at least one \(i_ 0\leq k\) such that \(Q_{i_ 0}(t)>0\) and \(\sigma_{i_ 0}(t)>0\); \(xf_ i(x)>0\) for \(x\neq 0\) and \(f_ i\) (\(i=0,\dots,k\)) are nondecreasing functions.