Multiple solutions of semi-linear elliptic equations on \(\mathbb{R}^ N\) (Q1340568)

The authors study the radial solutions of the equation \(-\Delta u=f(| x|)g(u)\) in \(\mathbb{R}^ n\), which includes the Makutuma equation and the scalar curvature equation as special cases. They introduce suitable assumptions on comparing the asymptotic behaviour of \(f\) and \(g\) at zero and at infinity, and prove the existence of a positive solution and a sequence of nodal solutions when \(g\) is odd. The results cover some previous ones in this direction.