Equicontinuity and normality of mappings with integrally bounded $p$-moduli

We consider the generic discrete open mappings in ${\mathbb{R}}^n$ under which the perturbation of extremal lengths of curve collections is controlled integrally via $\int Q(x){\eta }^p(\mathrm{\mid }x-x_0\mathrm{\mid })dm(x)$ with $n-1<p<n$, where $Q$ is a measurable function on ${\mathbb{R}}^n$ and $\int\limits_{r_1}^{r_2} \eta® dr \ge 1$forany$\eta$onagiveninterval$[r_1,r_2].$ We proved that the family of all open discrete mappings of above type is normal under appropriate restrictions on the majorant $Q\mathrm{.}$