A second order nonlinear differential inequality (Q1106377)

The author studies the differential inequality \((p(t)x^{'n^{*}})'- q(t)f(x)>0\) where \('=d/dt\), \(t\in [t_ 0,\infty)\), \(t_ 0\in {\mathbb{R}}\), \(n>0\), \(p,q>0\), \(p,q\in C(I)\), \(f\in C({\mathbb{R}})\), \(xf>0\), \(x\neq 0\), \(f(0)=0\), f is increasing and \(u^{^{*}}=| u|^ nsgn u\), \(u\in {\mathbb{R}}\). He proves that every solution is nonoscillatory and proves several theorems concerning the ultimately positive and ultimately negative solutions.