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Zbl 0766.49006
Ambrosetti, Antonio
Critical points and nonlinear variational problems. (English)
[J] Mém. Soc. Math. Fr., Nouv. Sér. 49, 139 p. (1992). ISSN 0249-633X

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.\par 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.
[J.F.Bonnans (Le Chesnay)]

MSC 2000:: *49J20 Optimal control problems with PDE (existence)
49J15 Optimal control problems with ODE (existence)

Keywords: Lusternik-Schnirelman theory; mountain-pass; linking theorems

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