Positive entire solutions of semilinear elliptic equations (Q1061925)

Elliptic equations of the form (*) \(\Delta u-m^ 2u+f(x,u)=0\) are considered in the entire space \(R^ n\). Conditions are given for the existence of two types of positive solutions of (*); one growing exponentially as \(| x| \to \infty\) and the other decaying to zero as \(| x| \to \infty\). Furthermore, uniqueness of decaying solutions is studied.