On the asymptotic behavior and radial symmetry of positive solutions of semilinear elliptic equations in \({\mathbb{R}{}}^ n\). I: Asymptotic behavior
The authors improve a previous paper [Arch. Ration. Mech. Anal. 108, No. 2, 175-194 (1989; Zbl 0705.35039)] proving the symmetry in \(\mathbb{R}^ N\) of any solution of the semilinear equation \(\Delta u+K(x)f(u)=0\) under suitable assymptions. The key new idea, in order to apply the ``moving plane'' process, is to obtain precise asymptotic expansions of solutions at infinity. Further extensions to more general equations and for domains other than the entire \(\mathbb{R}^ N\) are also given.
scientific article; zbMATH DE number 63709
scientific article