Infinitely many radial solutions of a semilinear elliptic problem on \(\mathbb{R}^ N\) (Q1311435)

The authors construct infinitely many radial solutions of the problem \(- \Delta u+ b(| x|)u= f(| x|,u)\) on \(\mathbb{R}^ N\) for suitable \(b\) and \(f\). They in fact prove that there is a solution with \(k\) zeros for any positive integer \(k\). They first construct positive and negative solutions and then construct the other solutions by a method of Nehari type [cf. \textit{Z. Nehari}, Acta Math. 105, 141-175 (1961; Zbl 0099.291)].