Multiplicity of solutions for semilinear variational inequalities via linking and \(\nabla\)-theorems (Q2506390)

The paper is concerned with study of existence of three distinct nontrivial solutions for a class of semilinear elliptic variational inequalities involving a superlinear nonlinearity, by combining the linking technique with that of \(\Delta\)-theorems. For the application of the linking theorem, this is related to the fact that the obstacles (\(\psi_1\) and \(\psi_2\)) are here just Borel functions, while for the application of the \(\Delta\)-theorems the problem would arise also for smooth obstacles. The authors adapt both theorems to a situation in which th global Palais-Smale condition is substituted by a local Palais-Smale condition combined with a quantitative gradient estimate on a suitable bounded set.