Eigenvalue problems for some variational inequalities with pointwise gradient constraint (Q1327581)

Summary: Some eigenvalue problems for elliptic semilinear variational inequalities are studied, the main feature being the presence of an obstacle of the first derivative of the unknown function. The role of a ``nontangency'' assumption is put into evidence: to have existence and multiplicity results one has to check that the convex set, produced by the obstacle condition, and the sphere in the function space, on which it seems natural to study eigenvalue problems, are not tangent. This condition is studied in some problems of the fourth and of the second order and some sufficient conditions for it are found, which allow to get results of existence and multiplicity.