| A special kind of linking which we call linking of deformation type is introduced in a finite dimensional setting and applied to obtain new critical point theorems. In particular, we give novel versions of the Saddle Point Theorem and the Generalized Mountain Pass Theorem. For functionals characterized by an infinite dimensional splitting our notion of linking is combined with an approximation argument to provide the existence of nontrivial solutions. For even functionals, this additional structure and our methods lead to the existence of multiple critical points. A general notion of linking is also introduced. The abstract results are applied repeatedly to study the existence of solution of elliptic boundary value problems and of Hamiltonian systems of ordinary differential equations. |
