Oscillation Criteria for Fourth-Order Nonlinear Dynamic Equations on Time Scales

Abstract

We establish some new oscillation criteria for nonlinear dynamic equation of the form $(a(t)(b(t)(c(t)x^{\mathrm{\Delta }}(t){)}^{\mathrm{\Delta }}{)}^{\mathrm{\Delta }}{)}^{\mathrm{\Delta }}+q(t)f(x(\sigma (t)))=\mathrm{0}$ on an arbitrary time scale $\mathbf{T}$ with $\text{s}\text{u}\text{p}\hspace{0.17em}\mathbf{T}=\mathrm{\infty }$, where $a(t),b(t),c(t)$ are positive rd-continuous functions. An example illustrating the importance of our result is included.