Properties of the positive solution of a semilinear elliptic partial differential equation in RnRn

A positive solution of a semilinear elliptic partial differential equation over the whole of RnRn is shown to be a regular decay function, i.e. u¯∈C2 and lim|x|→+∞u¯(x)=0, by means of the Sobolev embedding theorem and a bootstrap argument.