Given and , in this note, we are interested in construction of non-radial solutions for the following equation

in the whole space . The construction is basically due to Louis Dupaigne and mainly depends on the unique radial solution of the equation.

To start our construction, let us recall that there is a unique radial solution, denoted by , of the equation such that and . Moreover, is globally defined and blows up at infinity at a fixed rate

where and , see a paper by Yang and Guo published in *J. Partial Diff. Eqns.* in 2005.

Notice that

Hence, integrating both sides of the equation for gives

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