On the asymptotic behavior of radial entire solutions for the equation (−Δ)3u = up in Rn

Our main task in this note is to prove the existence and to classify the exact growth at infinity of radial positive C6-solutions of (−Δ)3u=up in Rn, where n⩾15 and p is bounded from below by the sixth-order Joseph-Lundgren exponent. Following the main work of Winkler, we introduce the sub- and super-solution method and comparison principle to conclude the asymptotic behavior of solutions.