Radial solutions of superlinear equations on \(\mathbb{R}^N\). I: A global variational approach (Q1580935)

The paper presents a global variational approach to the search for multiple nodal solutions \(u\in H^1 (\mathbb{R}^n)\) to a class of elliptic equations of type \[ -\Delta u(x)=f(|x|, u(x)), \] where \(f\) is superlinear and subcritical and \(f(|x|, 0)=0.\) The main result is the existence of a pair of nodal solutions with precisely \(k\) changes of sign in \(\mathbb{R}^n\), provided \(k\geq m\), where \(m\) is a (finite) Morse index of the ``linear part'' of the problem.