Oscillatory and asymptotic behavior of certain functional differential equations (Q1192764)

The equation (1) \(x^{(n)}(t)=P(t)x^{(n-1)}(t+\tau)+q(t)f(x(g(t)))\) is considered when \(n\) is odd, \(g,p,q:[t_ 0,+\infty)\to R\), \(f:\mathbb{R}\to\mathbb{R}\) are continuous, \(P(t)\geq 0\) and nonincreasing for \(t\geq t_ 0\), \(q(t)\geq 0\), \(\lim_{t\to+\infty}g(t)=+\infty\) and \(\tau\) is any real number. Sufficient conditions are given for every solution of (1) to be either oscillatory or \(x^{(i)}(t)\uparrow+\infty\) as \(t\uparrow+\infty\) \((i=0,\dots,n-1)\).