The authors study the semilinear elliptic equations
in an open bounded domain with Dirichlet boundary conditions, here .
Using variational methods they obtain the remarkable result: for and arbitrary there exists a sequence of solutions with negative energy converging to 0 as . Moreover, for and arbitrary there exists a sequence of solutions with unbounded energy. A similar result is obtained for first order Hamiltonian systems. The main ingredient in the proofs is a new critical point theorem, which guarantees the existence of infinitely many critical values of a functional with symmetries in a bounded range.