Asymptotic expansion of radial solutions for supercritical biharmonic equations

Abstract

Consider the positive, radial solutions of the nonlinear biharmonic equation ${\Delta }^{2}u=u^p$. There is a critical power $p_c$ such that solutions are linearly stable if and only if $p\ge p_c$. We obtain their asymptotic expansion at infinity in the case that $p\ge p_c$.