Forced oscillation of second-order superlinear dynamic equations on time scales

摘要

In this paper, by constructing a class of Philos type functions on time scales, we investigate the oscillation of the following second-order forced nonlinear dynamic equation $$x^{DeltaDelta}(t)-p(t)|x(q(t))|^{lambda-1}x(q(t))=e(t),quad tinmathbb{T}$$ where $mathbb{T}$ is a time scale, $p,e:mathbb{T}omathbb{R}$ are right dense continuous functions with $p>0$, $lambda>1$ is a constant, and $q(t)=t$ or $q(t)=sigma(t)$. Our results not only unify the oscillation of second-order forced differential equations and their discrete analogues, but also complement several results in the literature.