We prove the existence of three distinct nontrivial solutions for a class of semilinear elliptic vari- ational inequalities involving a superlinear nonlinearity. The approach is variational and is based on linking and $\nabla$-theorems. Some nonstandard adaptations are required to overcome the lack of the Palais–Smale condition.
Magrone, P., Mugnai, D., Servadei, R. (2006). Multiplicity of solutions for semilinear variational inequalities via linking and $nabla$-theorems. JOURNAL OF DIFFERENTIAL EQUATIONS, 228, 191-225.