On the asymptotic behavior of radial entire solutions for the equation $(-\Delta {)}^{3}u=u^p$ in ${\mathbf{R}}^n$

Abstract

Our main task in this note is to prove the existence and to classify the exact growth at infinity of radial positive $C^6$-solutions of $(-\Delta {)}^{3}u=u^p$ in ${\mathbf{R}}^n$, 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 comparision principle to conclude the asymptotic behavior of solutions.

26 pages

References in corpus (1)

• On the triharmonic Lane-Emden equation