FACHGEB The last decade has seen a tremendous development in critical
point theory in infinite dimensional spaces and its application to
nonlinear boundary value problems. In particular, striking results were
obtained in the classical problem of periodic solutions of Hamiltonian
systems. This book provides a systematic presentation of the most basic
tools of critical point theory: minimization, convex functions and
Fenchel transform, dual least action principle, Ekeland variational
principle, minimax methods, Lusternik- Schirelmann theory for Z2 and S1
symmetries, Morse theory for possibly degenerate critical points and
non-degenerate critical manifolds. Each technique is illustrated by
applications to the discussion of the existence, multiplicity, and
bifurcation of the periodic solutions of Hamiltonian systems. Among the
treated questions are the periodic solutions with fixed period or fixed
energy of autonomous systems, the existence of subharmonics in the
non-autonomous case, the asymptotically linear Hamiltonian systems, free
and forced superlinear problems. Application of those results to the
equations of mechanical pendulum, to Josephson systems of solid state
physics and to questions from celestial mechanics are given. The aim of
the book is to introduce a reader familiar to more classical techniques
of ordinary differential equations to the powerful approach of modern
critical point theory. The style of the exposition has been adapted to
this goal. The new topological tools are introduced in a progressive but
detailed way and immediately applied to differential equation problems.
The abstract tools can also be applied to partial differential equations
and the reader will also find the basic references in this direction in
the bibliography of more than 500 items which concludes the book.
ERSCHEIN
