Variational Methods: Applications to Nonlinear Partial Differential Equations and Hamiltonian Systems

The calculus of variations entered a new era when Hilbert spoke at the second International Congress of Mathematicians in Paris in 1900. This book follows the field from that point, through the work that brought large results in the decades that followed.

Among the milestones it mentions are the 1929 theorem of Ljusternik and Schnirelman, on three distinct prime closed geodesics on a compact surface of genus zero, and Douglas and Radó's answer to Plateau's problem in 1930/31. The author then applies the methods to nonlinear partial differential equations and Hamiltonian systems.

Published by Springer. ISBN-13: 9783540740124.