Local behavior of positive solutions to a nonlinear biharmonic equation near isolated singularities. (January 2022) - Wu, Ke
Abstract: In this paper, we consider the asymptotic behavior of positive solutions of the biharmonic equation Δ 2 u = u p in B 2 ∖ { 0 } with an isolated singularity, where the punctured ball B 2 ∖ { 0 } ⊂ R n with n > 5 and p > ( n + 4 ) / ( n − 4 ) . We classify isolated singularities of positive solutions and describe the asymptotic behavior of positive singular solutions without the sign assumption for − Δ u .