Citation/Abstract

The relative critical point theory and the relative critical groups in locally convex closed subsets of Banach manifolds are studied in this dissertation. We prove the strong deformation theorem for relatively differentiable function defined on locally convex subsets of Banach manifolds. We show that a Mountain-pass type theorem can be obtained and the relative critical groups can be discussed in our case.

The relative critical points of the energy functional give solutions of the minimal surface problem. We show that a Morse-Shiffman type theorem can be obtained in locally convex closed subsets of Banach manifolds.