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Critical points and nonlinear variational problems. (English) Zbl 0766.49006
This is an informal set of notes of 12 lectures given by Professor Ambrosetti at CEREMADE (University of Paris IX) in the frame of the “Chaire Lagrange”. The first part of the monograph is an introduction to the Lusternik-Schnirelman theory, the mountain-pass and the linking theorems. Sketches of some proofs are given. The second part deals with the application to several differential equations: semilinear elliptic boundary problems, some of them with discontinuous nonlinearities, vertex theory, conservative systems that include the classical problem of celestial mechanics; in particular the existence of periodic motions for the $$N$$-body problem is discussed.
The monograph can be recommended as it gives a concise introduction to a rather technical subject, bringing together the discussion of the general results of critical point theory and a wealth of applications.

##### MSC:
 49J20 Existence theories for optimal control problems involving partial differential equations 49J15 Existence theories for optimal control problems involving ordinary differential equations
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