Positive, Negative, and Nodal Solutions to Elliptic Differential Inclusions Depending on a Parameter

The homogeneous Dirichlet problem for a partial differential inclusion involving the p- Laplace operator and depending on a parameter λ > 0 is investigated. The existence of three smooth solutions, a smallest positive, a biggest negative, and a nodal one, is obtained for any λ sufficiently large by combining variational methods with truncation techniques.