The book provides an introduction to minimax methods in critical point theory and shows their use in existence questions for nonlinear differential equations. An expanded version of the author's 1984 CBMS lectures, this volume is the first monograph devoted solely to these topics. Among the abstract questions considered are the following: the mountain pass and saddle point theorems, multiple critical points for functionals invariant under a group of symmetries, perturbations from symmetry, and variational methods in bifurcation theory.

The book requires some background in functional analysis and differential equations, especially elliptic partial differential equations. It is addressed to mathematicians interested in differential equations and/or nonlinear functional analysis, particularly critical point theory.

Table of Contents

• An overview
• The mountain pass theorem and some applications
• Some variants of the mountain pass theorem
• The saddle point theorem
• Some generalizations of the mountain pass theorem
• Applications to Hamiltonian systems
• Functionals with symmetries and index theorems
• Multiple critical points of symmetric functionals: problems with constraints
• Multiple critical points of symmetric functionals: the unconstrained case
• Pertubations from symmetry
• Variational methods in bifurcation theory