Consider the second order superlinear dynamic equation
$$(*)\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{{x}^{\Delta \Delta }}(t)+p(t)f(x(\sigma (t)))=0$$
where
$p\,\in \,C(\mathbb{T},\,\mathbb{R})$
,
$\mathbb{T}$
is a time scale,
$f\,:\,\mathbb{R}\,\to \,\mathbb{R}$
is continuously differentiable and satisfies
${{f}^{'}}(x)>0$
, and
$x\,f\,(x)\,>\,0$
for
$x\,\ne \,0$
. Furthermore,
$f(x)$
also satisfies a superlinear condition, which includes the nonlinear function
$f(x)\,=\,{{x}^{\alpha }}$
with
$\alpha \,>\,1$
, commonly known as the Emden–Fowler case. Here the coefficient function
$p(t)$
is allowed to be negative for arbitrarily large values of
$t$
. In addition to extending the result of Kiguradze for
$\left( * \right)$
in the real case
$\mathbb{T}\,=\,\mathbb{R}$
, we obtain analogues in the difference equation and
$q$
-difference equation cases.