Nodal solutions to superlinear biharmonic equations via decomposition in dual cones

We present an abstract approach to locate multiple solutions of some superlinear variational problems in a Hilbert space $H$. The approach has many points in common with existing methods, but we add a new tool by using a decomposition technique related to dual cones in $H$ which goes back to Moreau. As an application we deduce new existence results for sign changing solutions for some superlinear biharmonic boundary value problems.