On the asymptotic behavior of solutions of Emden-Fowler equations on time scales (Q415449)

The authors study the second order dynamic equation \[ x^{\Delta\Delta}(t) + p(t) x^{\alpha}(t)=0, \] where \(\alpha\) is a quotient of two odd positive integers. It is proved that, under certain conditions, the equation has a solution \(x(t)\) with the property that \[ \lim_{t\to\infty}\frac{x(t)}{t}=A\neq 0. \]