A generalization of Opial's inequality and applications to second-order dynamic equations (Q609429)

The authors consider the second order dynamic equation of the form \[ y^{\Delta^2}+p(t)y^{\sigma}=0 \text{ for}\,\, t \in [a,b]_{T},\tag{\(*\)} \] where \(a, b \in \mathbb T\), \(p \in C_{rd}([a,b]_{\mathbb T},\mathbb R)\). The main results are given for disfocal problems together with an application on a nontrivial time scale. Also, the authors study the disconjugacy property of the solutions to equation \((*)\). Some examples are introduced to illustrate the main results.