Uniform a priori estimates for positive solutions of higher order Lane-Emden equations in $\mathbb{R}^n$

In this paper we study the existence of uniform a priori estimates for positive solutions to Navier problems higher order Lane–Emden equations \begin{equation}\label{0-0} (-\Delta)^{m}u(x)=u^{p}(x), \quad x\in\Omega, \end{equation} all large exponents $p$, where $\Omega\subset\mathbb{R}^{n}$ is star-shaped or strictly convex bounded domain with $C^{2m-2}$ boundary, $n\geq4$, and $2\leq m\leq\frac{n}{2}$. Our results extend those previous authors second $m=1$ general cases $m\geq2$.