Oscillation criteria for certain forced second-order nonlinear differential equations

Abstract

In this paper, two new oscillation criteria for forced second-order nonlinear differential equations of the form

$$\text{r(t)ψ(y(t))|y′(t)|}{}^{\mathrm{\alpha -1}}\text{y′(t)}\text{′ + q(t)f(y(t))=e(t), t≥t}{}_{\mathrm{o}}\text{,}$$

are established. Our results are based on the information on a sequence of subintervals of [t₀, ∞) only, rather than on the whole half-line. Our methodology is somewhat different from that of previous authors. The results presented here are much more general than a recent result of Li and Cheng [1].