Nodal and multiple solutions for nonlinear elliptic equations involving a reaction with zeros (Q2346009)

The authors are concerned with the quasilinear elliptic problem \(-\operatorname{div} a(\nabla u)=f(z,u)\) in a smooth and bounded domain \(\Omega\), complemented with homogeneous Dirichlet boundary condition. Here \(a:\mathbb R^N\to\mathbb R^N\) is a continuous, monotone mapping, \(f\) is a Carathéodory function. Under some additional hypotheses on \(a\) and \(f\) the authors obtain the existence of multiple solutions to the above problem. The approach relies on critical point theory combined with truncation arguments and Morse theory.