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Critical Point Theory and Hamiltonian Systems (Hardcover, 1989 ed.)
Loot Price: R4,921
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Critical Point Theory and Hamiltonian Systems (Hardcover, 1989 ed.)
Series: Applied Mathematical Sciences, 74
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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
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