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

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. View the MathML sourceu¯∈C2 and View the MathML sourcelim|x|→+∞u¯(x)=0, by means of the Sobolev embedding theorem and a bootstrap argument.