Forced oscillation of second-order superlinear dynamic equations on time scales - Yuangong Sun (Electronic Journal of Qualitative Theory of Differential Equations, 2011)
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 $$x^{\Delta\Delta}(t)-p(t)|x(q(t))|^{\lambda-1}x(q(t))=e(t),\quad t\in\mathbb{T}$$ where $\mathbb{T}$ is a time scale, $p,e:\mathbb{T}\to\mathbb{R}$ 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.