Asymptotic solutions of semilinear elliptic equations (Q791756)

Semilinear elliptic equations of the form \(Lu\equiv \Delta u-p(| x|)u+uf(x,u)=0\) are considered in exterior domains in \({\mathbb{R}}^ n\) for \(n\geq 2\). Both necessary and sufficient conditions are established for such equations to have positive solutions with prescribed asymptotic behavior as \(| x| \to \infty\).